Finite Group Databasebeta

← Group #13168609

Character table — Group #13168609

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122444446612121212121244444466612121212121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111-1-111-1-1-1-111-1-111111-1-11111111-1-111-1-11-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-111-111111-1-111-1-1-1-111111-11111-1-111-1-111-1-111-1-11-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-111-1-1-1-1111-11-1-11-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11-111
χ511111111111111111111111111111111111111111111111-11-1111-1-111111111-1-1-1-1-1-1-11-111-111-1-111111111-11-1-1-1-1-111-1-11-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-111-1-1-1-1-1-111-1-1-11-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1-1-1-111-1111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-11111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-111-1-1111-1-11-1-111-1-11111-1-1-1-1-11111-1-1-1-1-1-111-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111111111111-1-1-11-111-1-111-1-1-1-111-1-1-111-1-11111-1-11-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-11-11-1-11111-1-1-111-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111-1-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1111111111-1-1-1-111-1-1-111-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1111-11-1-11111-1-1-11-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1111111-1-1-1111-11-1-111-1-11111-1-1-1-1-111-1-11111-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-111-1-1-1-1-111-111-1-111-1-1-1-11111-11111-1-1-1-1-1-1111-1
χ17222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122202022002200002200-1-1-1-1200-1-12-1-1-1-100-1-100200-1-1-1-100000000
χ18222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-12-220-202200-2-20000-2-200-1-1-11200-11-2-1-111001100-200111100000000
χ19222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-22-2020-2-200220000-2-200111-1-2001-1211-1-100-1-100-200111100000000
χ20222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-20-20-2-200-2-2000022001111-20011-21111001100200-1-1-1-100000000
χ21222222-122-122-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-211111122-20-202200-2-200002200-1-1-11-2001-1211-1-1001100-200-1-11100000000
χ22222222-122-122-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-21111112-2-20202200220000-2-200-1-1-1-1-20011-2111100-1-10020011-1-100000000
χ23222222-122-122-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-2220-20-2-200-2-20000-2-2001111200-1-12-1-1-1-100110020011-1-100000000
χ24222222-122-122-1-1222-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-2-22020-2-2002200002200111-1200-11-2-1-11100-1-100-200-1-11100000000
χ2522222-12-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1202202-1-12200-1-10000222-1-10-1-12200-1-100-1-100-1-1002000000-1-10-100
χ2622222-12-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1202-20-2-1-1-2-200110000-2-22-1-10-11-2200-1-10011001100-2000000110100
χ2722222-12-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2202112200-1-10000-2-2-21101-12-2001100-1-100-1-100-2000000110100
χ2822222-12-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-20-211-2-20011000022-211011-2-2001100110011002000000-1-10-100
χ2922222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-1-211111-2-2111120-220-2-1-12200110000-2-22-1-101-1-2-2001100-1-10011002000000110-100
χ3022222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-1-211111-2-2111120-2-202-1-1-2-200-1-10000222-1-10112-20011001100-1-100-2000000-1-10100
χ3122222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-1-211111-2-21111-20220-211220011000022-2110-1-1-2200-1-100-1-1001100-2000000-1-10100
χ3222222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-1-211111-2-21111-202-20211-2-200-1-10000-2-2-2110-112200-1-1001100-1-1002000000110-100
χ332222-1222-122-122-12-1-122-1-122-1-12-1-122-1-1-1-1-1222-1-1-1-1-1-1-1-102022200-1-1-1-122220000000202-102-100-1-1-1-1-1-1-1-10200000-1-100-1000
χ342222-1222-122-122-12-1-122-1-122-1-12-1-122-1-1-1-1-1222-1-1-1-1-1-1-1-1020-22-20011-1-1-2-2-2-2000000020-2102-100-1-111-1-1110-20000011001000
χ352222-1222-122-122-12-1-122-1-122-1-12-1-122-1-1-1-1-1222-1-1-1-1-1-1-1-10-202-2200-1-11122-2-20000000-202-10-210011-1-111-1-10-20000011001000
χ362222-1222-122-122-12-1-122-1-122-1-12-1-122-1-1-1-1-1222-1-1-1-1-1-1-1-10-20-2-2-2001111-2-2220000000-20-210-2100111111110200000-1-100-1000
χ372222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-2-2-2111111110202-2-200-1-111-2-2-2-20000000-202102-100-1-1-1-1111102000001100-1000
χ382222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-2-2-211111111020-2-2200111122220000000-20-2-102-100-1-11111-1-10-200000-1-1001000
χ392222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-2-2-2111111110-2022-200-1-1-1-1-2-222000000020210-210011-1-1-1-1110-200000-1-1001000
χ402222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-2-2-2111111110-20-2220011-1-122-2-2000000020-2-10-21001111-1-1-1-102000001100-1000
χ412-2-22222-2-22-22-2-2-222220-2-2-22-2-2-222002-2-22000000000000000000000000002i−2i2i−2i2-2000000000000000000000002i−2i002i−2i2-20000
χ422-2-22222-2-22-22-2-2-222220-2-2-22-2-2-222002-2-22000000000000000000000000002i−2i−2i2i-2200000000000000000000000−2i2i002i−2i-220000
χ432-2-22222-2-22-22-2-2-222220-2-2-22-2-2-222002-2-2200000000000000000000000000−2i2i2i−2i-22000000000000000000000002i−2i00−2i2i-220000
χ442-2-22222-2-22-22-2-2-222220-2-2-22-2-2-222002-2-2200000000000000000000000000−2i2i−2i2i2-200000000000000000000000−2i2i00−2i2i2-20000
χ4544444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-211114-211-2-2-2-21111404000-2-2000000000000-2110-200-2001100000000000000000000000
χ4644444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-211114-211-2-2-2-21111-40-4000220000000000002-1-10200200-1-100000000000000000000000
χ4744444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-2221111-42-1-12222-1-1-1-140-4000-2-2000000000000-2110200200-1-100000000000000000000000
χ4844444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-2221111-42-1-12222-1-1-1-1-404000220000000000002-1-10-200-2001100000000000000000000000
χ494444-24-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-21111-24-2-2-2-21111110400400000-2-200000000000-20000-2-20011001100000000000000000
χ504444-24-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-21111-24-2-2-2-21111110-400-4000002200000000000200002200-1-100-1-100000000000000000
χ514444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-212211112-42222-1-1-1-1-1-10400-400000220000000000020000-2-2001100-1-100000000000000000
χ524444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-212211112-42222-1-1-1-1-1-10-400400000-2-200000000000-200002200-1-1001100000000000000000
χ534444-2-24-2-24-2-244-2-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-2111100040400-2-200-2-200000000000-2-20000000110011000000000000000
χ544444-2-24-2-24-2-244-2-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-21111000-40-40022002200000000000220000000-1-100-1-1000000000000000
χ554444-2-24-2-24-2-244-2-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-100040-400-2-2002200000000000-2200000001100-1-1000000000000000
χ564444-2-24-2-24-2-244-2-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-1000-404002200-2-2000000000002-20000000-1-10011000000000000000
χ5744-4-44444-4-4-4-44-44-444404-44-4-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-42-4-4-224-44-2-2042-22-4-22-4223−23-2-2220023−230023−232323−23−230000000000000000000000000000000000000000000000000000000
χ5944-4-444-24-42-4-4-224-44-2-2042-22-4-22-42−2323-2-22200−232300−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ6044-4-44-24-2-4-42-44-442-24-20-2-4-222422-400-2-222000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ6144-4-44-24-2-4-42-44-442-24-20-2-4-222422-400-2-2220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ6244-4-44-2-2-2-422-4-2242-2-210-221-12-2-12223−2311-1-100−330023−23−3−333000000−2i32i30000000000000i3−i300000003i−3i00000000000000000000000
χ6344-4-44-2-2-2-422-4-2242-2-210-221-12-2-12223−2311-1-100−330023−23−3−3330000002i3−2i30000000000000−i3i30000000−3i3i00000000000000000000000
χ6444-4-44-2-2-2-422-4-2242-2-210-221-12-2-122−232311-1-1003−300−232333−3−3000000−2i32i30000000000000i3−i30000000−3i3i00000000000000000000000
χ6544-4-44-2-2-2-422-4-2242-2-210-221-12-2-122−232311-1-1003−300−232333−3−30000002i3−2i30000000000000−i3i300000003i−3i00000000000000000000000
χ6644-4-4-24442-4-424-4-2-4-2-240-224-42-2-42200-2-222000000000000000000000023−2300000000000000000000000023−2300000000000000000
χ6744-4-4-24442-4-424-4-2-4-2-240-224-42-2-42200-2-2220000000000000000000000−2323000000000000000000000000−232300000000000000000
χ6844-4-4-24-2422-42-22-2-4-21-20-2-1-222122-123−2311-1-10023−2300−33−3−333000000000023−23000000000000000000003-300−3300000000000000000
χ6944-4-4-24-2422-42-22-2-4-21-20-2-1-222122-123−2311-1-10023−2300−33−3−3330000000000−232300000000000000000000-33003−300000000000000000
χ7044-4-4-24-2422-42-22-2-4-21-20-2-1-222122-1−232311-1-100−2323003−333−3−3000000000023−2300000000000000000000-3300−3300000000000000000
χ7144-4-4-24-2422-42-22-2-4-21-20-2-1-222122-1−232311-1-100−2323003−333−3−30000000000−2323000000000000000000003-3003−300000000000000000
χ724-44-4444-44-44-4-44-4-44440-44-4-44-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-4424-42-2-4-44-2-20-4-22242-2-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ744-44-444-2-4424-42-2-4-44-2-20-4-22242-2-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ754-44-44-2424-4-2-4-44-42-24-202422-2-4-22-400-22-2200000000000000000000000023−2300000000000000000000000023−23000000000000000
χ764-44-44-2424-4-2-4-44-42-24-202422-2-4-22-400-22-22000000000000000000000000−2323000000000000000000000000−2323000000000000000
χ774-44-4-244-4-2-442-442-4-2-2402-2-4-4-2242200-22-2200000000000000000000−2i32i3000000000000000000000000−2i32i30000000000000000000
χ784-44-4-244-4-2-442-442-4-2-2402-2-4-4-2242200-22-22000000000000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000
χ794-44-4-2-242-2-4-22-44221-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i00000000−2i32i30023−2300000000000000000000i3−i300−33000000000000000
χ804-44-4-2-242-2-4-22-44221-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i000000002i3−2i300−232300000000000000000000−i3i3003−3000000000000000
χ814-44-4-2-242-2-4-22-44221-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i00000000−2i32i300−232300000000000000000000i3−i3003−3000000000000000
χ824-44-4-2-242-2-4-22-44221-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i000000002i3−2i30023−2300000000000000000000−i3i300−33000000000000000
χ834-4-4444-2-4-4-2-4422-444-2-20-422-2-4224-200-222-200000000000000000000000000004i−4i0000000000000000000000000−2i2i0000000000
χ844-4-4444-2-4-4-2-4422-444-2-20-422-2-4224-200-222-20000000000000000000000000000−4i4i00000000000000000000000002i−2i0000000000
χ854-4-444-242-4424-4-4-4-2-24-202-42-22-42-2400-222-20000000000000000000000000000004-400000000000000000000000000000-220000
χ864-4-444-242-4424-4-4-4-2-24-202-42-22-42-2400-222-2000000000000000000000000000000-44000000000000000000000000000002-20000
χ874-4-44-244-424-4-2-4-424-2-24022-4422-4-2-200-222-2000000000000000000000000004i−4i0000000000000000000000000000000−2i2i000000
χ884-4-44-244-424-4-2-4-424-2-24022-4422-4-2-200-222-200000000000000000000000000−4i4i00000000000000000000000000000002i−2i000000
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
χ9188-8-8-4-48-44-8448-8-442-4-4024-44-2-44-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
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
χ948-88-88-4-4484-4-84-4-84-4-4204-4-2-2-44244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-8-44844-44-8-42-404244-4-2-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-44-44-444-4442220-22-2-22-22-2-200-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-44-444-4442220-22-2-22-22-2-200-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ988-8-888-4-44-8-44844-8-4-4-42044-2244-2-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-84-4-8-44448-42-404-24-44-24-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484484-4-8-84-42-4-40-244-4-2442-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-44-4444-42220-2-2-22-2-2-22200-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-44-4444-42220-2-2-22-2-2-22200-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000

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