Finite Group Databasebeta

← Group #13168623

Character table — Group #13168623

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124436661212121212121212121212122444466121212121212444444446661212121212121212121212121212121212241212121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111-1-11111-1-1-1-111-1-1111-111-1-11111-1-1-1-11111-11-1-1-1-1-1-111-1-1-11-1
χ31111111111111111111111111111111111111111111111111-111-11-1-111111111-1-1-1-1-1-1-1-1-111-1111-1-1-1111111111-111-1-1-1-1-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-111-1-111-1-1-1-11-1-1-11-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-1-1-111-1-1111111-1111-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-11-1-1-1111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111-11
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-11111-111
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111111-1-1-111-1-1-1-111-1-111-1-11-1-1-111-1-111111-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1111-111111-1-111-1-111-1-1-1-111-1-1-1-1111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-11-11-1-1-1111-1-11111-1-1-111111-1-1-1-111-11-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-1-1-111111-11-1111-1-1-111-1-1-1-111-111111-1-1-1-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111111-1-1-1-1-1-111-1-1-1-111111-1-1-11-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1111111-1-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-111-1-1111-1-1-111-1-111-1-11-11
χ17222222-122-1-1222-12-1-122-1-12-12-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-10220200-1-1-1-122220000000002-102-12000-1-1-1-1-1-1-1-120-1-100000000-100
χ18222222-122-1-1222-12-1-122-1-12-12-12-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-10-220-20011-1-122-2-2000000000-2-10-2120001111-1-1-1-1-201100000000100
χ19222222-122-1-1222-12-1-122-1-12-12-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-102-20200-1-111-2-2-2-20000000002102-1-2000-1-1-1-11111-201100000000100
χ20222222-122-1-1222-12-1-122-1-12-12-12-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-20-2001111-2-222000000000-210-21-20001111111120-1-100000000-100
χ21222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-222-1-1-1-11-2-2-21111111102-20-20011-1-122-2-2000000000-2102-1-2000-1-111-1-111201100000000-100
χ22222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-222-1-1-1-11-2-2-2111111110-2-20200-1-1-1-12222000000000210-21-200011-1-1-1-111-20-1-100000000100
χ23222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110220-2001111-2-222000000000-2-102-12000-1-11111-1-1-20-1-100000000100
χ24222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-2-2-2-1-1-1-11-2-2-2111111110-220200-1-111-2-2-2-20000000002-10-21200011-1-111-1-1201100000000-100
χ2522222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1220222222000000220022-1-1-1-10-1-1202-1-1-1-1-1-100000000-1-1-1-10000000
χ2622222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-12-202-222-2-2000000-2-200-2-2-1-1-110-11-202-1-111110000000011110000000
χ2722222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-220-22-2-222000000-2-200-2-2111-101-120-211-1-1-1-10000000011110000000
χ2822222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-2-2-2-2-20000002200221111011-20-211111100000000-1-1-1-10000000
χ2922222-122-1222-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-211-2-2111111220-2-222-2-2000000-2-20022-1-1-1101-120-211-1-11100000000-1-1110000000
χ3022222-122-1222-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-211-2-21111112-20-2222220000002200-2-2-1-1-1-1011-20-21111-1-10000000011-1-10000000
χ3122222-122-1222-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-2202-2-2-2-2-20000002200-2-211110-1-1202-1-1-1-1110000000011-1-10000000
χ3222222-122-1222-1-1222-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-211-2-2111111-2-2022-2-222000000-2-20022111-10-11-202-1-111-1-100000000-1-1110000000
χ332222-122-1222-1222-1-12-12-12-1-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-120220-1-10022-1-1000022002-1-102200-1-1-1-10000-1-1-1-102000000-1-1000-10
χ342222-122-1222-1222-1-12-12-12-1-1-12-12-12222-1-1-1-12-1-1-1-1-122-1-1-1-1-202-20110022-1-10000-2-200-21102-200-11110000-1-1-1-10-20000001100010
χ352222-122-1222-1222-1-12-12-12-1-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-120-220-1-100-2-2110000-2-2002-1-10-22001-1-1-1000011110-20000001100010
χ362222-122-1222-1222-1-12-12-12-1-1-12-12-122-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-201100-2-21100002200-2110-2-20011110000111102000000-1-1000-10
χ372222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-222-1-1-1-1-211111-2-2111120-2-20-1-10022-1-1000022002-1-10-2-20011110000-1-1110-2000000-1-100010
χ382222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-222-1-1-1-1-211111-2-21111-20-220110022-1-10000-2-200-2110-22001-1-1-10000-1-1110200000011000-10
χ392222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-21111202-20-1-100-2-2110000-2-2002-1-102-200-1111000011-1-10200000011000-10
χ402222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-2-2-2-1-1-1-1-211111-2-21111-202201100-2-21100002200-21102200-1-1-1-1000011-1-10-2000000-1-100010
χ412-22-2222-2-2-22-22-2-222220-22-2-2-2-22-22000022-2-200000000000000000000000002i−2i2i−2i2-20000000000000000000000002i−2i002i−2i2-200000
χ422-22-2222-2-2-22-22-2-222220-22-2-2-2-22-22000022-2-200000000000000000000000002i−2i−2i2i-220000000000000000000000002i−2i00−2i2i-2200000
χ432-22-2222-2-2-22-22-2-222220-22-2-2-2-22-22000022-2-20000000000000000000000000−2i2i2i−2i-22000000000000000000000000−2i2i002i−2i-2200000
χ442-22-2222-2-2-22-22-2-222220-22-2-2-2-22-22000022-2-20000000000000000000000000−2i2i−2i2i2-2000000000000000000000000−2i2i00−2i2i2-200000
χ452-2-22222-222-22-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-220000000000000000000002i−2i2i−2i0000002i−2i00000000000000002i−2i0000002i−2i00002-2000
χ462-2-22222-222-22-2-2-2-22220-2-2-222-2-22-2002i−2i2-2-220000000000000000000002i−2i2i−2i000000−2i2i00000000000000002i−2i000000−2i2i0000-22000
χ472-2-22222-222-22-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-22000000000000000000000−2i2i−2i2i0000002i−2i0000000000000000−2i2i0000002i−2i0000-22000
χ482-2-22222-222-22-2-2-2-22220-2-2-222-2-22-200−2i2i2-2-22000000000000000000000−2i2i−2i2i000000−2i2i0000000000000000−2i2i000000−2i2i00002-2000
χ4944444-2-24-2-2-24-2-2-24-21-24-21-2-2-21-21-2-2-2001111-24-2-2-2-21111110400400-2-2000000000000000-200-2-2000011110000000000000000000
χ5044444-2-24-2-2-24-2-2-24-21-24-21-2-2-21-21-2-2-2001111-24-2-2-2-21111110-400-40022000000000000000200220000-1-1-1-10000000000000000000
χ5144444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-21-21-2220011112-42222-1-1-1-1-1-10400-40022000000000000000200-2-2000011-1-10000000000000000000
χ5244444-2-24-2-2-24-2-2-24-21-2-4-21-2-2-21-21-2220011112-42222-1-1-1-1-1-10-400400-2-2000000000000000-200220000-1-1110000000000000000000
χ534444-24-2-24-2-2-244-2-21-2-241-2-21-2-2-2-2144441111-2-2-2-211-2-21111004000000-2-2-2-2000000000000-2000-200000001111000000000000000
χ544444-24-2-24-2-2-244-2-21-2-241-2-21-2-2-2-2144-4-41111-2-2-2-211-2-2111100-40000002222000000000000200020000000-1-1-1-1000000000000000
χ554444-24-2-24-2-2-244-2-21-2-2-41-2-21-2-2-2-21-4-44411112222-1-122-1-1-1-100-4000000-2-2-2-200000000000020002000000011-1-1000000000000000
χ564444-24-2-24-2-2-244-2-21-2-2-41-2-21-2-2-2-21-4-4-4-411112222-1-122-1-1-1-10040000002222000000000000-2000-20000000-1-111000000000000000
χ574444-2-24-2-244-2-2-24-2-2-214-2-21-21-21-2-2-2-20011114-211-2-2-2-2111140040-2-200000000000000-21100-2000-21100000000000000000000000
χ584444-2-24-2-244-2-2-24-2-2-214-2-21-21-21-2-2-2-20011114-211-2-2-2-21111-400-4022000000000000002-1-10020002-1-100000000000000000000000
χ594444-2-24-2-244-2-2-24-2-2-21-4-2-21-21-21-2-222001111-42-1-12222-1-1-1-1400-40-2-200000000000000-2110020002-1-100000000000000000000000
χ604444-2-24-2-244-2-2-24-2-2-21-4-2-21-21-21-2-222001111-42-1-12222-1-1-1-1-4004022000000000000002-1-100-2000-21100000000000000000000000
χ6144-4-44444-4-4-4-4-444-444404-44-4-44-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-24-422-4-44-2-4-2-240-2242-4-2-4220000-22-22000000000000000000023−230000000000000000000000000023−230000000000000000000
χ6344-4-444-24-422-4-44-2-4-2-240-2242-4-2-4220000-22-220000000000000000000−232300000000000000000000000000−23230000000000000000000
χ6444-4-44-2442-4-4-42-24-44-2-2042-2-42-222-423−2300-22-220023−230023−232323−23−2300000000000000000000000000000000000000000000000000000000
χ6544-4-44-2442-4-4-42-24-44-2-2042-2-42-222-4−232300-22-2200−232300−2323−23−23232300000000000000000000000000000000000000000000000000000000
χ6644-4-44-2-24222-42-2-2-4-21-20-2-1-22212-1223−23001-11-10023−2300−33−3−333000000023−230000000000000000000000003-3−330000000000000000000
χ6744-4-44-2-24222-42-2-2-4-21-20-2-1-22212-1223−23001-11-10023−2300−33−3−3330000000−2323000000000000000000000000-333−30000000000000000000
χ6844-4-44-2-24222-42-2-2-4-21-20-2-1-22212-12−2323001-11-100−2323003−333−3−3000000023−23000000000000000000000000-33−330000000000000000000
χ6944-4-44-2-24222-42-2-2-4-21-20-2-1-22212-12−2323001-11-100−2323003−333−3−30000000−23230000000000000000000000003-33−30000000000000000000
χ7044-4-4-244-2-4-4-42-4442-24-20-2-4-22242-420000-22-2200000000000000000−2i32i3000000000000000−2i32i300000000000000000000000000000000
χ7144-4-4-244-2-4-4-42-4442-24-20-2-4-22242-420000-22-22000000000000000002i3−2i30000000000000002i3−2i300000000000000000000000000000000
χ7244-4-4-2-24-22-4-422-242-2-210-2212-1-2-12223−23001-11-100−330023−23−3−33300000−2i32i3000000000000000i3−i300000003i−3i00000000000000000000000
χ7344-4-4-2-24-22-4-422-242-2-210-2212-1-2-12223−23001-11-100−330023−23−3−333000002i3−2i3000000000000000−i3i30000000−3i3i00000000000000000000000
χ7444-4-4-2-24-22-4-422-242-2-210-2212-1-2-122−2323001-11-1003−300−232333−3−300000−2i32i3000000000000000i3−i30000000−3i3i00000000000000000000000
χ7544-4-4-2-24-22-4-422-242-2-210-2212-1-2-122−2323001-11-1003−300−232333−3−3000002i3−2i3000000000000000−i3i300000003i−3i00000000000000000000000
χ764-44-444-2-4-42-2-44-424-2-2402-2-42-4242-20000-2-22200000000000000000000000004i−4i0000000000000000000000000000−2i2i00000000000
χ774-44-444-2-4-42-2-44-424-2-2402-2-42-4242-20000-2-2220000000000000000000000000−4i4i00000000000000000000000000002i−2i00000000000
χ784-44-44-24-42-44-4-22-444-2-20-4-22-422-2240000-2-2220000000000000000000000000004i−4i000000000000000000000000000000−2i2i0000000
χ794-44-44-24-42-44-4-22-444-2-20-4-22-422-2240000-2-222000000000000000000000000000−4i4i0000000000000000000000000000002i−2i0000000
χ804-44-4-2442-4-4424-4-4-2-24-2024222-4-2-4-20000-2-222000000000000000000000000000004-4000000000000000000000000000000-2200000
χ814-44-4-2442-4-4424-4-4-2-24-2024222-4-2-4-20000-2-22200000000000000000000000000000-440000000000000000000000000000002-200000
χ824-4-4444-2-44-224-4-42-4-2-24022-4-242-4-22004i−4i-222-2000000000000000000000−2i2i4i−4i000000000000000000000000−2i2i00000000000000000
χ834-4-4444-2-44-224-4-42-4-2-24022-4-242-4-2200−4i4i-222-20000000000000000000002i−2i−4i4i0000000000000000000000002i−2i00000000000000000
χ844-4-444-24-4-24-4422-4-44-2-20-4224-222-2-40000-222-200000000000000000000000000000004i−4i000000000000000000000000−2i2i000000000
χ854-4-444-24-4-24-4422-4-44-2-20-4224-222-2-40000-222-20000000000000000000000000000000−4i4i0000000000000000000000002i−2i000000000
χ864-4-44-244244-4-2-4-4-42-24-202-42-2-2-4242004i−4i-222-20000000000000000000004i−4i−2i2i000000000000000000000000−2i2i00000000000000000
χ874-4-44-244244-4-2-4-4-42-24-202-42-2-2-424200−4i4i-222-2000000000000000000000−4i4i2i−2i0000000000000000000000002i−2i00000000000000000
χ884-4-44-24-224-22-2-4-4221-2-20-1221-222-2-1004i−4i1-1-1100003-3003-33-3000000000−2i2i−2i2i000000000000000000000000i−i3i−3i000000000000000
χ894-4-44-24-224-22-2-4-4221-2-20-1221-222-2-1004i−4i1-1-110000-3300-33-33000000000−2i2i−2i2i000000000000000000000000i−i−3i3i000000000000000
χ904-4-44-24-224-22-2-4-4221-2-20-1221-222-2-100−4i4i1-1-1100003-3003-33-30000000002i−2i2i−2i000000000000000000000000−ii−3i3i000000000000000
χ914-4-44-24-224-22-2-4-4221-2-20-1221-222-2-100−4i4i1-1-110000-3300-33-330000000002i−2i2i−2i000000000000000000000000−ii3i−3i000000000000000
χ928888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9488-8-8-48-4-4-8444-88-442-4-4024-4-24-444-200002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-243−4300-11-1100−232300−232333−3−300000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-2−434300-11-110023−230023−23−3−33300000000000000000000000000000000000000000000000000000000
χ978-88-88-4-4-844-4-8-4448-42-4042444-2-4-2-4000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-48-44-84-448-84-42-4-40-2-44-244-442000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4844-884-44-8-4-4-4204-4-24-2424-4000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4444-44-444-42220-22-2-2-2-22-220000-1-1110000000033−33−333300000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4444-44-444-42220-22-2-2-2-22-220000-1-11100000000−333333−3300000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-8-4-448444-8-42-404-24-4-4-242400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-484-48-8-444-84-4-42044-2-424-2-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-4-44-444442220-2-2-222-2-22-20000-111-100006-600-33-3300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-4-44-444442220-2-2-222-2-22-20000-111-10000-66003-33-300000000000000000000000000000000000000000000000000000000

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