Finite Group Databasebeta

← Group #13169430

Character table — Group #13169430

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212366612121212121212121212121224444412121212121212124444446666121212121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111-1-1-1-111-1-111-1-111111-1111-11111-1-111-1-11-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111111111-1-1-1-11111-111-1-1111-1-111-1-111-11-1-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1111
χ511111111111111111111111111111111111111111111111-11-1111111111-1-1-1-1-1-111-1-1-1-111-1111-1-111111111-1-11-1-1-1-1-1-111-11-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-111-1-111-1-1-11-1-1-1-1-111-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-11111-1-1-1-111-1-1-1-1-1-1-11-1-1-11-1-1-1-111-1-1111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-11111111111-11-11-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-1-1-111-1-11111-1-1-11-11-1-111-1-1-1-111-11111-1-1-1-1-1-1111-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-11111-1-11-11-1-11111-1-1-111-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-1-11111111-1-1-111-1-1-1-1-1-1111111-1-1-111-1-1111-1-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-111-1-1-1-1-1111-1-1111111-1-1-1-111-1-1-111-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1111-11-1-11111-1-1-11-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-111-1-1-1-1-1-1111-11-111-1-11111-1-1-11111-1-1-1-1-1-111-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111111111-1-1-1-11-11-11111-1-1-1-11111-1-1-111-1-11111-1-11-1
χ17222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1222020220000220022002-1-1-1-10-1-120-1-1-1-100-1-100200-1-1-1-100000000
χ18222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-12-220-20-2-200002200-2-2002-1-1-110-11-20-1-111001100-200111100000000
χ19222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-22-2020220000-2-200-2-200-2111-101-12011-1-100-1-100-200111100000000
χ20222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-20-20-2-20000-2-2002200-21111011-201111001100200-1-1-1-100000000
χ21222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-211111122-20-20220000-2-20022002-1-1-1101-1-2011-1-1001100-200-1-11100000000
χ22222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-21111112-2-2020-2-20000-2-200-2-2002-1-1-1-101120111100-1-10020011-1-100000000
χ23222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-2220-202200002200-2-200-211110-1-1-20-1-1-1-100110020011-1-100000000
χ24222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-2-22020-2-2000022002200-2111-10-1120-1-11100-1-100-200-1-11100000000
χ2522222-1222-12-122-12-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-12022020022-1-1-1-1220000-12-1-10-12002-1-100-1-100-1-10200000-1-100-1000
χ2622222-1222-12-122-12-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1202-20-200-2-211-1-1-2-20000-12-1-101200-2-1-1001100110-20000011001000
χ2722222-1222-12-122-12-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-20-22020022-1-111-2-200001-2110-1-20021100-1-100-1-10-20000011001000
χ2822222-1222-12-122-12-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-20-200-2-211112200001-21101-200-211001100110200000-1-100-1000
χ2922222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-2111120-220-200221111220000-12-1-10-1-200-21100-1-100110-200000-1-1001000
χ3022222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-2111120-2-20200-2-2-1-111-2-20000-12-1-101-200211001100-1-102000001100-1000
χ3122222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-21111-20220-2002211-1-1-2-200001-2110-1200-2-1-100-1-1001102000001100-1000
χ3222222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-21111-202-20200-2-2-1-1-1-12200001-211012002-1-1001100-1-10-200000-1-1001000
χ332222-122-1-1222222-1-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1020222-1-1-1-1220000002200002202-1-100-1-1-1-1-1-1-1-1002000000-1-10-100
χ342222-122-1-1222222-1-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1020-22-2-1-111-2-2000000-2-200002-202-1100-1-111-1-11100-2000000110100
χ352222-122-1-1222222-1-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10-202-2211-1-122000000-2-20000-220-21-10011-1-111-1-100-2000000110100
χ362222-122-1-1222222-1-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10-20-2-2-21111-2-2000000220000-2-20-2110011111111002000000-1-10-100
χ372222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-2111111110202-2-2-1-1-1-1-2-2000000220000-22021100-1-1-1-1111100-2000000-1-10100
χ382222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-211111111020-2-22-1-11122000000-2-20000-2-2021-100-1-11111-1-1002000000110-100
χ392222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-2111111110-2022-211-1-1-2-2000000-2-20000220-2-110011-1-1-1-111002000000110-100
χ402222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-2111111110-20-2221111220000002200002-20-2-1-1001111-1-1-1-100-2000000-1-10100
χ412-2-22222-2-222-2-2-2-222220-2-2-22-2-2-222002-2-22000000000000000000000000002i−2i2i−2i2-2000000000000000000000002i−2i002i−2i2-20000
χ422-2-22222-2-222-2-2-2-222220-2-2-22-2-2-222002-2-22000000000000000000000000002i−2i−2i2i-2200000000000000000000000−2i2i002i−2i-220000
χ432-2-22222-2-222-2-2-2-222220-2-2-22-2-2-222002-2-2200000000000000000000000000−2i2i2i−2i-22000000000000000000000002i−2i00−2i2i-220000
χ442-2-22222-2-222-2-2-2-222220-2-2-22-2-2-222002-2-2200000000000000000000000000−2i2i−2i2i2-200000000000000000000000−2i2i00−2i2i2-20000
χ4544444-2-244-2-2-2-2-2-24-2-214-2-211-2-21-2-2-2-21111-2411-2-2-2-21111404000000000-2-2000000-2-21100-20001100000000000000000000000
χ4644444-2-244-2-2-2-2-2-24-2-214-2-211-2-21-2-2-2-21111-2411-2-2-2-21111-40-40000000002200000022-1-1002000-1-100000000000000000000000
χ4744444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-21-2-22211112-4-1-12222-1-1-1-140-400000000022000000-2-211002000-1-100000000000000000000000
χ4844444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-21-2-22211112-4-1-12222-1-1-1-1-404000000000-2-200000022-1-100-20001100000000000000000000000
χ494444-24-2-2-24-24-2-24-2-21-24-21-2-2-21-2-21-2-211114-2-2-2-2-2111111040040-2-20000000000000000-200-2-200011001100000000000000000
χ504444-24-2-2-24-24-2-24-2-21-24-21-2-2-21-2-21-2-211114-2-2-2-2-21111110-400-4022000000000000000020022000-1-100-1-100000000000000000
χ514444-24-2-2-24-24-2-24-2-21-2-4-21-2-2-21-2-21221111-422222-1-1-1-1-1-10400-40-2-20000000000000000200-220001100-1-100000000000000000
χ524444-24-2-2-24-24-2-24-2-21-2-4-21-2-2-21-2-21221111-422222-1-1-1-1-1-10-40040220000000000000000-2002-2000-1-1001100000000000000000
χ534444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-2111100040400-2-2-2-20000000000000-2000-20000110011000000000000000
χ544444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-21111000-40-40022220000000000000200020000-1-100-1-1000000000000000
χ554444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-100040-400-2-2220000000000000-2000200001100-1-1000000000000000
χ564444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-1000-4040022-2-200000000000002000-20000-1-10011000000000000000
χ5744-4-44444-4-4-4-44-44-444404-44-4-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-4-42-4-224-44-2-2042-22-4-22-4223−23-2-2220023−230023−232323−23−230000000000000000000000000000000000000000000000000000000
χ5944-4-444-24-4-42-4-224-44-2-2042-22-4-22-42−2323-2-22200−232300−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ6044-4-44-244-42-424-4-2-4-24-20-2-4-222422-400-2-22200000000000000000000000023−23000000000000000023−2300000000000000000000000
χ6144-4-44-244-42-424-4-2-4-24-20-2-4-222422-400-2-222000000000000000000000000−23230000000000000000−232300000000000000000000000
χ6244-4-44-2-24-4222-22-2-4-2-210-221-12-2-12223−2311-1-100−330023−23−3−33300000000000023−23000000003-3000000−3300000000000000000000000
χ6344-4-44-2-24-4222-22-2-4-2-210-221-12-2-12223−2311-1-100−330023−23−3−333000000000000−232300000000-330000003−300000000000000000000000
χ6444-4-44-2-24-4222-22-2-4-2-210-221-12-2-122−232311-1-1003−300−232333−3−300000000000023−2300000000-33000000−3300000000000000000000000
χ6544-4-44-2-24-4222-22-2-4-2-210-221-12-2-122−232311-1-1003−300−232333−3−3000000000000−2323000000003-30000003−300000000000000000000000
χ6644-4-4-244-22-4-4-44-442-2-240-224-42-2-42200-2-222000000000000000000−2i32i3000000000000000000000000−2i32i3000000000000000000000
χ6744-4-4-244-22-4-4-44-442-2-240-224-42-2-42200-2-2220000000000000000002i3−2i30000000000000000000000002i3−2i3000000000000000000000
χ6844-4-4-24-2-22-42-4-2242-21-20-2-1-222122-123−2311-1-10023−2300−33−3−333000000−2i32i3000000000000000000000000i3−i3003i−3i00000000000000000
χ6944-4-4-24-2-22-42-4-2242-21-20-2-1-222122-123−2311-1-10023−2300−33−3−3330000002i3−2i3000000000000000000000000−i3i300−3i3i00000000000000000
χ7044-4-4-24-2-22-42-4-2242-21-20-2-1-222122-1−232311-1-100−2323003−333−3−3000000−2i32i3000000000000000000000000i3−i300−3i3i00000000000000000
χ7144-4-4-24-2-22-42-4-2242-21-20-2-1-222122-1−232311-1-100−2323003−333−3−30000002i3−2i3000000000000000000000000−i3i3003i−3i00000000000000000
χ724-44-4444-44-4-44-44-4-44440-44-4-44-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-44-4242-2-4-44-2-20-4-22242-2-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ744-44-444-2-44-4242-2-4-44-2-20-4-22242-2-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ754-44-44-24-442-4-2-442-4-24-202422-2-4-22-400-22-22000000000000000000000023−230000000000000000000000000023−23000000000000000
χ764-44-44-24-442-4-2-442-4-24-202422-2-4-22-400-22-220000000000000000000000−232300000000000000000000000000−2323000000000000000
χ774-44-4-2442-2-4-44-44-42-2-2402-2-4-4-2242200-22-2200000000000000000000−2i32i3000000000000000000000000−2i32i30000000000000000000
χ784-44-4-2442-2-4-44-44-42-2-2402-2-4-4-2242200-22-22000000000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000
χ794-44-4-2-242-22-4-2-44221-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i00000000−2i32i323−230000000000000000000000i3−i300−33000000000000000
χ804-44-4-2-242-22-4-2-44221-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i000000002i3−2i3−23230000000000000000000000−i3i3003−3000000000000000
χ814-44-4-2-242-22-4-2-44221-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i00000000−2i32i3−23230000000000000000000000i3−i3003−3000000000000000
χ824-44-4-2-242-22-4-2-44221-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i000000002i3−2i323−230000000000000000000000−i3i300−33000000000000000
χ834-4-4444-2-4-44-2-422-444-2-20-422-2-4224-200-222-200000000000000000000000000004i−4i0000000000000000000000000−2i2i0000000000
χ844-4-4444-2-4-44-2-422-444-2-20-422-2-4224-200-222-20000000000000000000000000000−4i4i00000000000000000000000002i−2i0000000000
χ854-4-444-24-4-4-242-4-424-24-202-42-22-42-2400-222-2000000000000000000000000004i−4i0000000000000000000000000000000−2i2i000000
χ864-4-444-24-4-4-242-4-424-24-202-42-22-42-2400-222-200000000000000000000000000−4i4i00000000000000000000000000000002i−2i000000
χ874-4-44-2442244-4-4-4-4-2-2-24022-4422-4-2-200-222-20000000000000000000000000000004-400000000000000000000000000000-220000
χ884-4-44-2442244-4-4-4-4-2-2-24022-4422-4-2-200-222-2000000000000000000000000000000-44000000000000000000000000000002-20000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-48-444-848-8-442-4-4024-44-2-44-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-44444-44-4422202-22-2-22-2-2-243−43-1-11100−232300−232333−3−30000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44444-44-4422202-22-2-22-2-2-2−4343-1-1110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-8844-44-44-8-4-4204-4-2-2-44244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-44-4-8484-4-84-42-404244-4-2-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-44-444-44-4442220-22-2-22-22-2-200-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-444-44-4442220-22-2-22-22-2-200-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-8-8-4-444448-4-42044-2244-2-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4448-4-844-8-4-42-404-24-44-24-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-484-8-84-42-4-40-244-4-2442-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-44444-42220-2-2-22-2-2-22200-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-44444-42220-2-2-22-2-2-22200-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000

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