Finite Group Databasebeta

← Group #13168226

Character table — Group #13168226

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212223666121212121212121212121212444446666121212124466121212121212121212121212121212121212244441212121212121212446122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111-1-11-1111111-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-11111111-1-111-1-1111-1-1-1111111-1-1-1-11111-11-1-11-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-111111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111-1-1-111111-11-1-111111111-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-11-1-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-111111-11-1-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111111111111-11-1-11-1-1-1-1-111-1-111-1-1-1-11-111111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-111-11-1-1-11-11-1-111-1-1-1-111-1111-111-1-111-1-1-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-1-1111-1-1-1-1-1-1-11111-1-11-1-111-1-1-1-11111-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-111-11-11-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-11111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1111111-1-111-1-11-11-11111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-1-1-1-1-111-1-1-11111111-1-1-1-1111-1-111-1-1-1-11111111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-11-1111-11-111-1-11111-1-1-1111-111-1-111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-11-111-111111-1-111-1-111-1-11-111111-1-111-1-1-1-11
χ17222222-122-1-1222-122-1-122-1-12-1-1-12-12222-1-1-1-1-1222-1-1-1-1-1-1-1-12220022-1-1-1-10000-1-1-122-10020-1-1-1-1-1-1000020200-1-100000000-100
χ18222222-122-1-1222-122-1-122-1-12-1-1-12-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-220022-1-1110000-1-1-1-2-210020-1-111110000-20-2001100000000100
χ19222222-122-1-1222-122-1-122-1-12-1-1-12-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-122-200-2-211-1-1000011122-100-2011-1-1-1-10000-20-2001100000000100
χ20222222-122-1-1222-122-1-122-1-12-1-1-12-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-200-2-211110000111-2-2100-20111111000020200-1-100000000-100
χ21222222-122-1-1222-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-11-2-2-2111111112-2-20022-1-1-1-10000-1-112-2100-2011-1-1110000-20200-1-100000000100
χ22222222-122-1-1222-122-1-1-22-1-12-1-1-12-1-2-222-1-1-1-11-2-2-211111111-22-20022-1-1110000-1-11-22-100-201111-1-1000020-2001100000000-100
χ23222222-122-1-1222-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-11-2-2-2111111112-2200-2-211-1-1000011-12-210020-1-1-1-111000020-2001100000000-100
χ24222222-122-1-1222-122-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-11-2-2-211111111-22200-2-21111000011-1-22-10020-1-111-1-10000-20200-1-100000000100
χ2522222-12-1222-1222-1-12-12-12-1-12-1-1-122222-1-1-1-12-1-1-122-1-1-1-1-1-100222-1-12200-1-100-1-1200022-1-1-1-10000-1-1-1-102002000000-1-1000-10
χ2622222-12-1222-1222-1-12-12-12-1-12-1-1-122222-1-1-1-12-1-1-122-1-1-1-1-1-1002-2-2-1-122001100-1-12000-2-2-11-1-1000011110-200-20000001100010
χ2722222-12-1222-1222-1-12-12-12-1-12-1-1-1222-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100-22211-2-200-1-10011-2000221-1110000-1-1-1-10-200-20000001100010
χ2822222-12-1222-1222-1-12-12-12-1-12-1-1-1222-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100-2-2-211-2-200110011-2000-2-211110000111102002000000-1-1000-10
χ2922222-12-1222-1222-1-12-1-2-12-1-12-1-1-12-2-222-1-1-1-1-2111-2-211111100-22-2-1-12200-1-100-1-1-20002-211110000-1-1110-2002000000-1-100010
χ3022222-12-1222-1222-1-12-1-2-12-1-12-1-1-12-2-222-1-1-1-1-2111-2-211111100-2-22-1-122001100-1-1-2000-221-111000011-1-10200-200000011000-10
χ3122222-12-1222-1222-1-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-1-2111-2-21111110022-211-2-200-1-1001120002-2-11-1-10000-1-1110200-200000011000-10
χ3222222-12-1222-1222-1-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-1-2111-2-2111111002-2211-2-2001100112000-22-1-1-1-1000011-1-10-2002000000-1-100010
χ332222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1220220000222222000-1-12-1-10200-1-1-1-1-1-1-1-10002000-1-1-1-10000000
χ342222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1220-2-2000022-2-2-2-2000-1-12110-200-1-1-1-11111000-200011110000000
χ352222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-20220000-2-222-2-200011-2-1-102001111-1-1-1-1000-200011110000000
χ362222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-20000-2-2-2-22200011-2110-200111111110002000-1-1-1-10000000
χ372222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211112-202-20000222222000-11-2-110-200-1-111-1-111000-2000-1-1110000000
χ382222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211112-20-22000022-2-2-2-2000-11-21-10200-1-11111-1-1000200011-1-10000000
χ392222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-21111-2202-20000-2-222-2-20001-12-110-20011-1-1-1-111000200011-1-10000000
χ402222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-21111-220-220000-2-2-2-2220001-121-1020011-1-111-1-1000-2000-1-1110000000
χ412-22-22222-2-2-2-22-22-222202-22-2-2-2-2-22002-222-2-2000000000000000002-22-200002i−2i2-200000000000000000000000002i−2i00002i−2i000
χ422-22-22222-2-2-2-22-22-222202-22-2-2-2-2-22002-222-2-2000000000000000002-22-20000−2i2i2-20000000000000000000000000−2i2i0000−2i2i000
χ432-22-22222-2-2-2-22-22-222202-22-2-2-2-2-2200-2222-2-200000000000000000-22-2200002i−2i-2200000000000000000000000002i−2i0000−2i2i000
χ442-22-22222-2-2-2-22-22-222202-22-2-2-2-2-2200-2222-2-200000000000000000-22-220000−2i2i-220000000000000000000000000−2i2i00002i−2i000
χ4544444-2-2-24-2-2-244-2-2-2-214-2-21-2-211-2-244441111-2-2-2-2-2-211111100400-2-2-2-200000011-200000-201100000000000000000000000000
χ4644444-2-2-24-2-2-244-2-2-2-214-2-21-2-211-2-244-4-41111-2-2-2-2-2-211111100-4002222000000-1-120000020-1-100000000000000000000000000
χ4744444-2-2-24-2-2-244-2-2-2-21-4-2-21-2-211-2-2-4-4441111222222-1-1-1-1-1-100-400-2-2-2-20000001120000020-1-100000000000000000000000000
χ4844444-2-2-24-2-2-244-2-2-2-21-4-2-21-2-211-2-2-4-4-4-41111222222-1-1-1-1-1-1004002222000000-1-1-200000-201100000000000000000000000000
χ494444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-2-21-2-2001111-24-2-211-2-21111440000000-2-20000000-2-2-200000011110000000000000000000000
χ504444-24-24-2-2-24-2-2-24-21-24-21-2-21-2-2-21-2-2001111-24-2-211-2-21111-4-40000000220000000222000000-1-1-1-10000000000000000000000
χ514444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-2-21220011112-422-1-122-1-1-1-14-40000000-2-20000000-22200000011-1-10000000000000000000000
χ524444-24-24-2-2-24-2-2-24-21-2-4-21-2-21-2-2-21220011112-422-1-122-1-1-1-1-4400000002200000002-2-2000000-1-1110000000000000000000000
χ534444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-21-2-2-20011114-211-2-2-2-2111100044000000-2-200000000-2-20-20000001111000000000000000000
χ544444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-21-2-2-20011114-211-2-2-2-21111000-4-400000022000000002202000000-1-1-1-1000000000000000000
χ554444-2-24-2-244-2-2-24-21-2-2-41-2-21-2-2-21-222001111-42-1-12222-1-1-1-10004-4000000-2-200000000-220200000011-1-1000000000000000000
χ564444-2-24-2-244-2-2-24-21-2-2-41-2-21-2-2-21-222001111-42-1-12222-1-1-1-1000-4400000022000000002-20-2000000-1-111000000000000000000
χ5744-4-4444-444-44-4-4-4-44440-4-4-4444-4-4-400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-224-4-42-44-2-20-4224-2-22-420000-222-200000000000000000000023−23000000000000000023−23000000000000000000000000
χ5944-4-444-2-44-224-4-42-44-2-20-4224-2-22-420000-222-2000000000000000000000−23230000000000000000−2323000000000000000000000000
χ6044-4-44-24244-4-2-4-4-42-24-202-42-24-222-40000-222-20000000000000000000000023−2300000000000000000023−2300000000000000000000
χ6144-4-44-24244-4-2-4-4-42-24-202-42-24-222-40000-222-200000000000000000000000−2323000000000000000000−232300000000000000000000
χ6244-4-4-244-4-24-4422-4-4-2-24022-4-2-24-422−2i32i300-222-200−2i32i3−2i32i300−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ6344-4-4-244-4-24-4422-4-4-2-24022-4-2-24-4222i3−2i300-222-2002i3−2i32i3−2i3002i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ6444-4-4-24-2-4-2-224222-4-21-202-12-21-222-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i300000000023−230000000000000000−333i−3i0000000000000000000000
χ6544-4-4-24-2-4-2-224222-4-21-202-12-21-222-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i3000000000−232300000000000000003−3−3i3i0000000000000000000000
χ6644-4-4-24-2-4-2-224222-4-21-202-12-21-222-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i300000000023−230000000000000000−33−3i3i0000000000000000000000
χ6744-4-4-24-2-4-2-224222-4-21-202-12-21-222-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i3000000000−232300000000000000003−33i−3i0000000000000000000000
χ6844-4-4-2-242-24-4-222-421-2-20-1221-2-22-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i30000000000023−23000000000000000000−333i−3i000000000000000000
χ6944-4-4-2-242-24-4-222-421-2-20-1221-2-22-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i300000000000−23230000000000000000003−3−3i3i000000000000000000
χ7044-4-4-2-242-24-4-222-421-2-20-1221-2-22-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i30000000000023−23000000000000000000−33−3i3i000000000000000000
χ7144-4-4-2-242-24-4-222-421-2-20-1221-2-22-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i300000000000−23230000000000000000003−33i−3i000000000000000000
χ724-44-444-24-422-44-4-2-44-2-2042-2-4222-4-2004-4-2-222000000000000000004-4-22000000-22000000000000000000000000000000000000
χ734-44-444-24-422-44-4-2-44-2-2042-2-4222-4-200-44-2-22200000000000000000-442-20000002-2000000000000000000000000000000000000
χ744-44-44-24-2-4-4-424-442-24-20-2-4-22-42224004-4-2-22200000000000000000-224-4000000-22000000000000000000000000000000000000
χ754-44-44-24-2-4-4-424-442-24-20-2-4-22-4222400-44-2-222000000000000000002-2-440000002-2000000000000000000000000000000000000
χ764-44-44-2-2-2-42224-4-22-2-210-22122-1-12-2004-411-1-10000003i−3i3i−3i3i−3i00000-22-220000001-1000000003i−3i00000000000000000000000000
χ774-44-44-2-2-2-42224-4-22-2-210-22122-1-12-2004-411-1-1000000−3i3i−3i3i−3i3i00000-22-220000001-100000000−3i3i00000000000000000000000000
χ784-44-44-2-2-2-42224-4-22-2-210-22122-1-12-200-4411-1-10000003i−3i3i−3i3i−3i000002-22-2000000-1100000000−3i3i00000000000000000000000000
χ794-44-44-2-2-2-42224-4-22-2-210-22122-1-12-200-4411-1-1000000−3i3i−3i3i−3i3i000002-22-2000000-11000000003i−3i00000000000000000000000000
χ804-44-4-24442-4-4-4-224-4-2-240-22422-4-42-20000-2-22200000000000000000000000004i−4i000000000000000000000000000−2i2i000000000
χ814-44-4-24442-4-4-4-224-4-2-240-22422-4-42-20000-2-2220000000000000000000000000−4i4i0000000000000000000000000002i−2i000000000
χ824-4-44444-4-4-44-4-44-444440-44-4-4-4-444-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-4-42-2-4-44244-2-20-4-22-422-2420000-22-22000000000000000000000000000000000000000000000000000023−2300000000000
χ844-4-4444-2-4-42-2-4-44244-2-20-4-22-422-2420000-22-220000000000000000000000000000000000000000000000000000−232300000000000
χ854-4-444-242-4-442-44-4-2-24-202422-42-2-2-40000-22-220000000000000000000000000000000000000000000000000000000000−2i32i300000
χ864-4-444-242-4-442-44-4-2-24-202422-42-2-2-40000-22-2200000000000000000000000000000000000000000000000000000000002i3−2i300000
χ874-4-44-244-42-44-42-2-44-2-2402-2-422-44-220000-22-220000000000000000000000000000000000000000000000000000000023−230000000
χ884-4-44-244-42-44-42-2-44-2-2402-2-422-44-220000-22-2200000000000000000000000000000000000000000000000000000000−23230000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-448-44-4-8-844-4-42044-2-4-42-24400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-44-4-44-444442220-2-2-2222-2-2-2−4i34i300-111-1002i3−2i32i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-44-444442220-2-2-2222-2-2-24i3−4i300-111-100−2i32i3−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ948-88-8-48-48444-8-44-4-8-42-40-4-2-44-24442000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-48-44-8-84-44842-4-4024-4-2444-2-4000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-44444-44-4422202-22-2-2-2-2-220000-1-1110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-44444-44-4422202-22-2-2-2-2-220000-1-111000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ988-8-888-4-44-84-44-884-4-4-4204-4-244-22-4400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-844-4-84-448-42-404244-24-4-4-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8844-4-8-42-4-40-2-44-244-42400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-44-42220-22-2-2-2-222-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-44-42220-22-2-2-2-222-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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