Finite Group Databasebeta

← Group #13168108

Character table — Group #13168108

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order122233366666666633346666666661212121212121212443666121212121212121212222446666121212121212121212121212121212122266666666661212121244444664412121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-11-111-1-11111111111111111-1-1-1111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111111111111111111111111111-1-1111-1-1111111111111111111-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ51111111111111111111111111111111111111-1-11111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111-1-11-1-1-1-1-1
χ61111111111111111111111111111111111111-1-1111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-111-111-1-11
χ71111111111111111111111111111111111111-1-11111111111111-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1111
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11-11-1-11111-11-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-111-1-111111-1-111-1-1-1-11-111-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-11111-1-111-1-1-1-1-111-11-1-1-1-111-1-111
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-11-11-11111-1-11-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-11111-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-11-11-111-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11-1-1-1-111-1-11111-111-11-1-11111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-11111-1-111-1-1-1-11-1-111-1-1111-111-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-11111111-11-1-111-1-1-11-11-11
χ17222222-1-122-12-12222-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122202-1-1-1-1000000000000000022222-1-1-1-1-1-1-1-12-1-100002-1-100-100000
χ18222222-1-122-12-12222-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-122-20-2-1-1110000000000000000-2-2-222-111-1-1-1-11-2110000-21100100000
χ19222222-1-122-12-12222-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-220211-1-10000000000000000-2-22-2-21-1-11111-12-1-10000-21100100000
χ20222222-1-122-12-12222-1-12-1-1-12-1-122-12222222200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-21111000000000000000022-2-2-211111111-21100002-1-100-100000
χ21222222-1-122-12-12222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-220-2-1-1-1-100000000000000002222-21-1-1-1-1111-2110000-2-1-100100000
χ22222222-1-122-12-12222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-11111111112-2-202-1-1110000000000000000-2-2-22-2111-1-111-12-1-1000021100-100000
χ23222222-1-122-12-12222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-2220-211-1-10000000000000000-2-22-22-1-1-111-1-11-211000021100-100000
χ24222222-1-122-12-12222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-200-1-1-1-1111111111-22-2021111000000000000000022-2-22-11111-1-1-12-1-10000-2-1-100100000
χ2522222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1220202200-1-1-1-12222-1-1-1-1-1-1-1-1000-1-1200-1-1-1-10000220000000000-1-10
χ2622222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-2-2020-2-200-1-1-1-12222-1-1-1-1-1-1-1-100011-20011110000-2-20000000000110
χ2722222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1220-2022001111-2-2-2-211111111000-1-1200-1-1-1-10000-2-20000000000110
χ2822222-122-1-122222-1-12-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-20-20-2-2001111-2-2-2-21111111100011-20011110000220000000000-1-10
χ2922222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-211111122-1-1-1-1-2-2-21111112-20-202200-1-111-2-222-1-1-1-11111000-11-200-1-11100002-20000000000-110
χ3022222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-211111122-1-1-1-1-2-2-2111111-220-20-2-200-1-111-2-222-1-1-1-111110001-120011-1-10000-2200000000001-10
χ3122222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-2111111-2-2-1-1-1-1-2-2-21111112-2020220011-1-122-2-21111-1-1-1-1000-11-200-1-1110000-2200000000001-10
χ3222222-122-1-122222-1-12-1-22-1-1-12-1-1-12-2-2111111-2-2-1-1-1-1-2-2-2111111-22020-2-20011-1-122-2-21111-1-1-1-10001-120011-1-100002-20000000000-110
χ332222-1222222-12-1-12-1-122-122-1-12-1-1-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-10022200222222-1-1-1-1-1-1-1-1-1-1-1-100-1000-1-100002-1-1-10022000000-1-1000
χ342222-1222222-12-1-12-1-122-122-1-12-1-1-1-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-100-22-200-2-22222-1-1-1-1-1-1-1-1-1-1-1-1001000110000-211100-2-200000011000
χ352222-1222222-12-1-12-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1002-220022-2-2-2-211111111111100-1000-1-100002-1-1-100-2-200000011000
χ362222-1222222-12-1-12-1-122-122-1-12-1-1-1-1-122-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-100-2-2-200-2-2-2-2-2-2111111111111001000110000-21110022000000-1-1000
χ372222-1222222-12-1-12-1-12-2-122-1-12-1-1-111-2-2111122-1-1-1-1-211-2-21111002-2-2002222-2-211-1-1-1-1-1-1111100-1000-1-10000-2111002-2000000-11000
χ382222-1222222-12-1-12-1-12-2-122-1-12-1-1-111-2-2111122-1-1-1-1-211-2-2111100-2-2200-2-222-2-211-1-1-1-1-1-111110010001100002-1-1-100-220000001-1000
χ392222-1222222-12-1-12-1-12-2-122-1-12-1-1-111-2-21111-2-2-1-1-1-1-211-2-211110022-20022-2-222-1-1111111-1-1-1-100-1000-1-10000-211100-220000001-1000
χ402222-1222222-12-1-12-1-12-2-122-1-12-1-1-111-2-21111-2-2-1-1-1-1-211-2-2111100-22200-2-2-2-222-1-1111111-1-1-1-10010001100002-1-1-1002-2000000-11000
χ4122-2-2222-22-222-2-2-2-22220-22-2-2-2-22-22000000002i−2i22-2-20000000000000000002i−2i00002i−2i2i2i−2i−2i00002-200000000000000000002-22i−2i000000
χ4222-2-2222-22-222-2-2-2-22220-22-2-2-2-22-22000000002i−2i22-2-20000000000000000002i−2i00002i−2i2i2i−2i−2i0000-220000000000000000000-22−2i2i000000
χ4322-2-2222-22-222-2-2-2-22220-22-2-2-2-22-2200000000−2i2i22-2-2000000000000000000−2i2i0000−2i2i−2i−2i2i2i00002-200000000000000000002-2−2i2i000000
χ4422-2-2222-22-222-2-2-2-22220-22-2-2-2-22-2200000000−2i2i22-2-2000000000000000000−2i2i0000−2i2i−2i−2i2i2i0000-220000000000000000000-222i−2i000000
χ4544444-2-2-2-2-2-24-244-2-2-214-211-2-21-2-2-244-2-2-2-2-2-2001111-2-2-211111144000-2-2000000000000000000000-2-2-20011110000000000000000000
χ4644444-2-2-2-2-2-24-244-2-2-214-211-2-21-2-2-244-2-2-2-2-2-2001111-2-2-2111111-4-40002200000000000000000000022200-1-1-1-10000000000000000000
χ4744444-2-2-2-2-2-24-244-2-2-21-4-211-2-21-2-2-2-4-4222222001111222-1-1-1-1-1-14-4000-2-2000000000000000000000-2220011-1-10000000000000000000
χ4844444-2-2-2-2-2-24-244-2-2-21-4-211-2-21-2-2-2-4-4222222001111222-1-1-1-1-1-1-44000220000000000000000000002-2-200-1-1110000000000000000000
χ494444-24-2-244-2-2-2-2-24-21-241-2-2-21-2-2-21-2-244-2-2-2-2001111-211-2-211110040400-2-2000000000000000000-2000110000-2-211000000000000000
χ504444-24-2-244-2-2-2-2-24-21-241-2-2-21-2-2-21-2-244-2-2-2-2001111-211-2-2111100-40-400220000000000000000002000-1-1000022-1-1000000000000000
χ514444-24-2-244-2-2-2-2-24-21-2-41-2-2-21-2-2-2122-4-422220011112-1-122-1-1-1-10040-400-2-2000000000000000000-200011000022-1-1000000000000000
χ524444-24-2-244-2-2-2-2-24-21-2-41-2-2-21-2-2-2122-4-422220011112-1-122-1-1-1-100-40400220000000000000000002000-1-10000-2-211000000000000000
χ534444-2-244-2-24-24-2-2-21-2-24-2-2-21-2-211-2-2-2-2-211114411114-2-2-2-21111000400000-2-2-2-2-2-2-2-2111111110000000000000000000000000000000
χ544444-2-244-2-24-24-2-2-21-2-24-2-2-21-2-211-2-2-2-2-21111-4-411114-2-2-2-21111000-40000022222222-1-1-1-1-1-1-1-10000000000000000000000000000000
χ554444-2-244-2-24-24-2-2-21-2-2-4-2-2-21-2-211-22222-1-1-1-1441111-42222-1-1-1-1000-400000-2-22222-2-21111-1-1-1-10000000000000000000000000000000
χ564444-2-244-2-24-24-2-2-21-2-2-4-2-2-21-2-211-22222-1-1-1-1-4-41111-42222-1-1-1-100040000022-2-2-2-222-1-1-1-111110000000000000000000000000000000
χ5744-4-444-224-4-242-4-4-44-2-202-22-4224-4-20000000000-2-22200000000000000000000000000000000004-40000000000000000000-2200000000
χ5844-4-444-224-4-242-4-4-44-2-202-22-4224-4-20000000000-2-2220000000000000000000000000000000000-4400000000000000000002-200000000
χ5944-4-44-24-4-2244-4-4-42-24-20-4-222-42-224000000004i−4i-2-222000000000000000000−2i2i00004i−4i−2i−2i2i2i00000000000000000000000000000000000
χ6044-4-44-24-4-2244-4-4-42-24-20-4-222-42-22400000000−4i4i-2-2220000000000000000002i−2i0000−4i4i2i2i−2i−2i00000000000000000000000000000000000
χ6144-4-4-244-44-44-2-422-4-2-24024-422-4-22-2000000004i−4i-2-2220000000000000000004i−4i0000−2i2i−2i−2i2i2i00000000000000000000000000000000000
χ6244-4-4-244-44-44-2-422-4-2-24024-422-4-22-200000000−4i4i-2-222000000000000000000−4i4i00002i−2i2i2i−2i−2i00000000000000000000000000000000000
χ6344-4-4-2-24-4-224-2-42221-2-202-22-1221-1-200003i3i−3i−3i4i−4i11-1-1000003i3i−3i−3i000000000−2i2i0000−2i2iii−i−i33-3-30000000000000000000000000000000
χ6444-4-4-2-24-4-224-2-42221-2-202-22-1221-1-200003i3i−3i−3i−4i4i11-1-1000003i3i−3i−3i0000000002i−2i00002i−2i−i−iii-3-3330000000000000000000000000000000
χ6544-4-4-2-24-4-224-2-42221-2-202-22-1221-1-20000−3i−3i3i3i4i−4i11-1-100000−3i−3i3i3i000000000−2i2i0000−2i2iii−i−i-3-3330000000000000000000000000000000
χ6644-4-4-2-24-4-224-2-42221-2-202-22-1221-1-20000−3i−3i3i3i−4i4i11-1-100000−3i−3i3i3i0000000002i−2i00002i−2i−i−iii33-3-30000000000000000000000000000000
χ674-44-44444-4-4-4-4-44-444440-4-4-4444-4-4-400000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-2-4-42-424-444-2-202224-2-2-4-420000000000-222-200000000000000−2i32i300000000000000000000000000−2i32i3000000000000000000000
χ694-44-444-2-2-4-42-424-444-2-202224-2-2-4-420000000000-222-2000000000000002i3−2i3000000000000000000000000002i3−2i3000000000000000000000
χ704-44-44-24422-4-4-44-4-2-24-20-422-24-222-400−2i32i3−2i32i3−2i32i300-222-2000−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ714-44-44-24422-4-4-44-4-2-24-20-422-24-222-4002i3−2i32i3−2i32i3−2i300-222-20002i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ724-44-44-2-2-2222-424-4-2-2-2102-1-1-2-2122200−2i32i3−2i32i3−2i32i3001-1-11000i3−i3i3−i3i3−i300000−2i32i300000000000000000000000000i3−i33-30000000000000000000
χ734-44-44-2-2-2222-424-4-2-2-2102-1-1-2-2122200−2i32i3−2i32i3−2i32i3001-1-11000i3−i3i3−i3i3−i3000002i3−2i300000000000000000000000000−i3i3-330000000000000000000
χ744-44-44-2-2-2222-424-4-2-2-2102-1-1-2-21222002i3−2i32i3−2i32i3−2i3001-1-11000−i3i3−i3i3−i3i300000−2i32i300000000000000000000000000i3−i3-330000000000000000000
χ754-44-44-2-2-2222-424-4-2-2-2102-1-1-2-21222002i3−2i32i3−2i32i3−2i3001-1-11000−i3i3−i3i3−i3i3000002i3−2i300000000000000000000000000−i3i33-30000000000000000000
χ764-44-4-2444-4-4-42-4-224-2-2402-4-4-2-242220000000000-222-2000000000000000000000023−2300000023−2323−230000000000000000000000000000000
χ774-44-4-2444-4-4-42-4-224-2-2402-4-4-2-242220000000000-222-20000000000000000000000−2323000000−2323−23230000000000000000000000000000000
χ784-44-4-2-24422-42-4-22-21-2-202221-2-2-1-1200−2i32i3i3−i3i3−i3001-1-11000−2i32i3i3−i3i3−i3000000000000023−23003i−3i3i−3i−33−330000000000000000000000000000000
χ794-44-4-2-24422-42-4-22-21-2-202221-2-2-1-1200−2i32i3i3−i3i3−i3001-1-11000−2i32i3i3−i3i3−i30000000000000−232300−3i3i−3i3i3−33−30000000000000000000000000000000
χ804-44-4-2-24422-42-4-22-21-2-202221-2-2-1-12002i3−2i3−i3i3−i3i3001-1-110002i3−2i3−i3i3−i3i3000000000000023−2300−3i3i−3i3i−33−330000000000000000000000000000000
χ814-44-4-2-24422-42-4-22-21-2-202221-2-2-1-12002i3−2i3−i3i3−i3i3001-1-110002i3−2i3−i3i3−i3i30000000000000−2323003i−3i3i−3i3−33−30000000000000000000000000000000
χ824-4-44444-4-44-4-44-44-444404-44-4-4-4-44-400000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-22-442-4-2-44-44-2-20-22-2-422-4420000000000-22-220000000000000000−2i32i30000000000000000000000−2i32i300000000000000000000000
χ844-4-4444-22-442-4-2-44-44-2-20-22-2-422-4420000000000-22-2200000000000000002i3−2i300000000000000000000002i3−2i300000000000000000000000
χ854-4-444-24-42-2-4-44-442-24-2042-22-422-2-40000000000-22-220000000000000000000023−230000000023−23−23230000000000000000000000000000000
χ864-4-444-24-42-2-4-44-442-24-2042-22-422-2-40000000000-22-2200000000000000000000−232300000000−232323−230000000000000000000000000000000
χ874-4-44-244-4-44-4242-2-4-2-240-2-4422-42-2223−230023−23−232300-22-22023−230023−23−232300000000000000000000000000000000000000000000000000000000
χ884-4-44-244-4-44-4242-2-4-2-240-2-4422-42-22−232300−232323−2300-22-220−232300−232323−2300000000000000000000000000000000000000000000000000000000
χ894-4-44-24-22-4422-22-2-4-21-2012-22-122-2-123−230023−23−2323001-11-10−3300−333−30000000−2i32i30000000000000000000000i3−i30000003i−3i000000000000000
χ904-4-44-24-22-4422-22-2-4-21-2012-22-122-2-123−230023−23−2323001-11-10−3300−333−300000002i3−2i30000000000000000000000−i3i3000000−3i3i000000000000000
χ914-4-44-24-22-4422-22-2-4-21-2012-22-122-2-1−232300−232323−23001-11-103−3003−3−330000000−2i32i30000000000000000000000i3−i3000000−3i3i000000000000000
χ924-4-44-24-22-4422-22-2-4-21-2012-22-122-2-1−232300−232323−23001-11-103−3003−3−3300000002i3−2i30000000000000000000000−i3i30000003i−3i000000000000000
χ934-4-44-2-24-42-2-4242-221-2-20-22-2-122-11223−2300−333−3001-11-1023−2300−333−30000000000023−230000-333-3−333−30000000000000000000000000000000
χ944-4-44-2-24-42-2-4242-221-2-20-22-2-122-11223−2300−333−3001-11-1023−2300−333−300000000000−232300003-3-333−3−330000000000000000000000000000000
χ954-4-44-2-24-42-2-4242-221-2-20-22-2-122-112−2323003−3−33001-11-10−2323003−3−330000000000023−2300003-3-33−333−30000000000000000000000000000000
χ964-4-44-2-24-42-2-4242-221-2-20-22-2-122-112−2323003−3−33001-11-10−2323003−3−3300000000000−23230000-333-33−3−330000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-44-44-484-8-84-4-42042-244-2-44-4000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-448-8-4-4444-8-42-40-2-444-24-442000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-44-4-444442220-22-2-2-2-22-2200006i6i−6i−6i00-1-11100000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-44-4-444442220-22-2-2-2-22-220000−6i−6i6i6i00-1-111000003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4-4-8-8444-448-42-40-244-42-444-200000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-444444-44-42220-2-2-2222-2-2-200−4i34i32i3−2i32i3−2i300-111-10002i3−2i3−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4-444444-44-42220-2-2-2222-2-2-2004i3−4i3−2i32i3−2i32i300-111-1000−2i32i3i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1068-8-888-4-444-44-8-4-884-4-420-4-2244-24-4400000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-444-44-4422202-22-2-2-2-22-243−4300−232323−2300-11-110−2323003−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-444-44-4422202-22-2-2-2-22-2−43430023−23−232300-11-11023−2300−333−300000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).