Finite Group Databasebeta

← Group #13168267

Character table — Group #13168267

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122444446612121212121222444466612121212121212121212121212121212122446612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111-1-1-1-1-1-111-1-11111-11-11111111-1-111-1-1-11-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-111111-1-11111-1-1-1-111111-11-111-1111-1-111-1-111-1-11-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111111111111111111-1-1-11-111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11-1111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-11-111
χ511111111111111111111111111111111111111111111111-1111-11-1-111111111-1-1-1-1-1-1-11111-11-1-1-1111111111-1-111-1-1-1-1-1-11-1-1-1
χ611111111111111111111111111111111111111111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-11-11-1-11-1-1-111-1-111-1-1-1-11-1-1-1-1-1-111-1111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-11111-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-111-11-1-1-11111-1-1-1-111
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
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-1-1-111-1-11111-1-11-11-1-1-111-1-1-1-1111-11-1-111-1-1-1-111-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111111111111-1-1-11-1-1-11111-1-1-1-1-1-1-11111-1-111-1-11-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-111-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-111-1-1-1-111111-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-1-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-111-1-1-1-1-1-111-1-1-11-1-111111111-1-1-1-11111-1-1-1-1-111111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-11111-1-111-1-1-11-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1111111-1-1-1-1-1111-1111-1-1-1-11111-1-1-11111-1-111-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-111-1-1-1-1-1-111-11-1111-1-11111-1-11-11-1-111-1-1-1-1111-1
χ17222222-12-1-122-1222-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-102220200-1-1-1-122220000000-1-12202000-1-1-1-1-1-1-1-1200-1-1000000-1000
χ18222222-12-1-122-1222-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1022-20-200-1-111-2-2-2-20000000-112-202000-1-111-1-111-200110000001000
χ19222222-12-1-122-1222-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10-2-22020011-1-122-2-200000001-1-220-200011-1-111-1-1-200110000001000
χ20222222-12-1-122-1222-1-122-1-122-1-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-20-2001111-2-222000000011-2-20-200011111111200-1-1000000-1000
χ21222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-21111111102-220-20011-1-1-2-2-2-20000000-11-2202000-1-11111-1-120011000000-1000
χ22222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-21111111102-2-20200111122220000000-1-1-2-202000-1-1-1-11111-200-1-10000001000
χ23222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-2111111110-2220-200-1-1-1-1-2-222000000011220-20001111-1-1-1-1-200-1-10000001000
χ24222222-12-1-122-1222-1-12-2-1-122-1-12-1-1-2-2-1-1-1-1-21-2-2111111110-22-20200-1-11122-2-200000001-12-20-200011-1-1-1-11120011000000-1000
χ2522222-122222-12-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122202022220000002200-1-1-120-10-1-12-1-1-1-100-1-10002000-1-1-1-1000000
χ2622222-122222-12-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-12-2-202022-2-2000000-2-200-1-1-1-2010-112-1-1110011000-20001111000000
χ2722222-122222-12-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2220-20-2-222000000-2-20011120-101-1-211-1-100-1-1000-20001111000000
χ2822222-122222-12-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-20-20-2-2-2-20000002200111-201011-2111100110002000-1-1-1-1000000
χ2922222-122222-12-1-122-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-211111122-20-2022-2-20000002200-1-1-120101-1-211-1-10011000-2000-1-111000000
χ3022222-122222-12-1-122-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-21111112-220-202222000000-2-200-1-1-1-20-1011-2111100-1-1000200011-1-1000000
χ3122222-122222-12-1-122-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-22-2020-2-2-2-2000000-2-2001112010-1-12-1-1-1-10011000200011-1-1000000
χ3222222-122222-12-1-122-1-1-22-1-1-12-1-12-111-1-1-1-1-2-211-2-2111111-2-22020-2-2220000002200111-20-10-112-1-11100-1-1000-2000-1-111000000
χ332222-122-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1200222-1-10022-1-10000222-1-1020-120-1-1-100-1-100-1-1002000000-1-10-100
χ342222-122-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1200-22-2-1-100-2-2110000-2-22-1-10-20120-1-1-10011001100-2000000110100
χ352222-122-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-2002-22110022-1-10000-2-2-211020-1-2011100-1-100-1-100-2000000110100
χ362222-122-122-12222-1-12-12-12-1-1-12-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-1-200-2-2-21100-2-211000022-2110-201-2011100110011002000000-1-10-100
χ372222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-211112002-2-2-1-10022110000-2-22-1-10-20-1-20111001100-1-1002000000110-100
χ382222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-21111200-2-22-1-100-2-2-1-10000222-1-10201-2011100-1-1001100-2000000-1-10100
χ392222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-21111-20022-211002211000022-2110-20-120-1-1-1001100-1-100-2000000-1-10100
χ402222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-1-1-1-11-21111-2-21111-200-2221100-2-2-1-10000-2-2-211020120-1-1-100-1-10011002000000110-100
χ412-22-2222-2-2-2222-2-2-22220-2-2-22-2-2-222002-2-22000000000000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i002i−2i0000
χ422-22-2222-2-2-2222-2-2-22220-2-2-22-2-2-222002-2-22000000000000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i00−2i2i0000
χ432-22-2222-2-2-2222-2-2-22220-2-2-22-2-2-222002-2-2200000000000000000000000000-222i−2i−2i2i00000000000000000000000-222i−2i00−2i2i0000
χ442-22-2222-2-2-2222-2-2-22220-2-2-22-2-2-222002-2-2200000000000000000000000000-22−2i2i2i−2i00000000000000000000000-22−2i2i002i−2i0000
χ4544444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-211114-2-2-2-2-211111104400000-2-20000000000000-20-200-200011001100000000000000000
χ4644444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-211114-2-2-2-2-21111110-4-400000220000000000000202002000-1-100-1-100000000000000000
χ4744444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-21221111-422222-1-1-1-1-1-104-400000220000000000000-20200-20001100-1-100000000000000000
χ4844444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-21221111-422222-1-1-1-1-1-10-4400000-2-2000000000000020-2002000-1-1001100000000000000000
χ494444-24-2-2-2-2-24-244-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-211110004040000-2-2-2-20000000000-20-20000000110011000000000000000
χ504444-24-2-2-2-2-24-244-21-2-241-2-2-21-2-21-2441111-2-2-2-211-2-21111000-40-40000222200000000002020000000-1-100-1-1000000000000000
χ514444-24-2-2-2-2-24-244-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-100040-40000-2-222000000000020-20000000-1-10011000000000000000
χ524444-24-2-2-2-2-24-244-21-2-2-41-2-2-21-2-21-2-4-411112222-1-122-1-1-1-1000-404000022-2-20000000000-20200000001100-1-1000000000000000
χ534444-2-24-244-2-24-2-2-2-2-214-2-211-2-21-2-2-2-21111-2411-2-2-2-21111400040-2-2000000000000-2110000-20-21100000000000000000000000
χ544444-2-24-244-2-24-2-2-2-2-214-2-211-2-21-2-2-2-21111-2411-2-2-2-21111-4000-40220000000000002-1-10000202-1-100000000000000000000000
χ554444-2-24-244-2-24-2-2-2-2-21-4-2-211-2-21-2-22211112-4-1-12222-1-1-1-14000-40-2-2000000000000-2110000202-1-100000000000000000000000
χ564444-2-24-244-2-24-2-2-2-2-21-4-2-211-2-21-2-22211112-4-1-12222-1-1-1-1-400040220000000000002-1-10000-20-21100000000000000000000000
χ5744-4-444444-4-4-4-44-4-444404-44-4-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-22-4-424-4-4-2-240-224-42-2-42200-2-2220000000000000000000023−230000000000000000000000000023−2300000000000000000
χ5944-4-444-24-22-4-424-4-4-2-240-224-42-2-42200-2-22200000000000000000000−232300000000000000000000000000−232300000000000000000
χ6044-4-44-2444-4-42-4-22-44-2-2042-22-4-22-4223−23-2-2220023−230023−232323−23−230000000000000000000000000000000000000000000000000000000
χ6144-4-44-2444-4-42-4-22-44-2-2042-22-4-22-42−2323-2-22200−232300−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ6244-4-44-2-24-22-422-22-4-21-20-2-1-222122-123−2311-1-10023−2300−33−3−3330000000023−2300000000000000000000003-300−3300000000000000000
χ6344-4-44-2-24-22-422-22-4-21-20-2-1-222122-123−2311-1-10023−2300−33−3−33300000000−23230000000000000000000000-33003−300000000000000000
χ6444-4-44-2-24-22-422-22-4-21-20-2-1-222122-1−232311-1-100−2323003−333−3−30000000023−230000000000000000000000-3300−3300000000000000000
χ6544-4-44-2-24-22-422-22-4-21-20-2-1-222122-1−232311-1-100−2323003−333−3−300000000−232300000000000000000000003-3003−300000000000000000
χ6644-4-4-244-24-42-4-44-42-24-20-2-4-222422-400-2-222000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ6744-4-4-244-24-42-4-44-42-24-20-2-4-222422-400-2-2220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ6844-4-4-2-24-24-422-4-222-2-210-221-12-2-12223−2311-1-100−330023−23−3−333000000−2i32i30000000000000i3−i300000003i−3i00000000000000000000000
χ6944-4-4-2-24-24-422-4-222-2-210-221-12-2-12223−2311-1-100−330023−23−3−3330000002i3−2i30000000000000−i3i30000000−3i3i00000000000000000000000
χ7044-4-4-2-24-24-422-4-222-2-210-221-12-2-122−232311-1-1003−300−232333−3−3000000−2i32i30000000000000i3−i30000000−3i3i00000000000000000000000
χ7144-4-4-2-24-24-422-4-222-2-210-221-12-2-122−232311-1-1003−300−232333−3−30000002i3−2i30000000000000−i3i300000003i−3i00000000000000000000000
χ724-44-444-2-42244-2-4-4-4-2-24022-4422-4-2-200-222-2000000000000000000000000004-4000000000000000000000000000-220000000000
χ734-44-444-2-42244-2-4-4-4-2-24022-4422-4-2-200-222-200000000000000000000000000-440000000000000000000000000002-20000000000
χ744-44-44-24-4-4-44-2422-44-2-20-422-2-4224-200-222-200000000000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ754-44-44-24-4-4-44-2422-44-2-20-422-2-4224-200-222-20000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ764-44-4-2442-4-4-244-4-42-24-202-42-22-42-2400-222-20000000000000000000000000000004i−4i00000000000000000000000000000−2i2i0000
χ774-44-4-2442-4-4-244-4-42-24-202-42-22-42-2400-222-2000000000000000000000000000000−4i4i000000000000000000000000000002i−2i0000
χ784-4-44444-4-44-4-4-4-4444440-44-4-44-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-42-2-4-42-444-2-2402-2-4-4-2242200-22-22000000000000000000000023−230000000000000000000000000023−23000000000000000
χ804-4-4444-2-42-2-4-42-444-2-2402-2-4-4-2242200-22-220000000000000000000000−232300000000000000000000000000−2323000000000000000
χ814-4-444-24-4-44-42-42-244-2-20-4-22242-2-4200-22-220000000000000000000000000000000000000000000000000000000000023−23000000
χ824-4-444-24-4-44-42-42-244-2-20-4-22242-2-4200-22-2200000000000000000000000000000000000000000000000000000000000−2323000000
χ834-4-44-2442-442-4-4-44-2-24-202422-2-4-22-400-22-22000000000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000
χ844-4-44-2442-442-4-4-44-2-24-202422-2-4-22-400-22-220000000000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000
χ854-4-44-24-222-22-42-44-21-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i000000000023−23−2i32i300000000000000000000i3−i300−33000000000000000
χ864-4-44-24-222-22-42-44-21-2-20-1-22212-2-12001-11-100003i−3i003i−3i3i−3i0000000000−23232i3−2i300000000000000000000−i3i3003−3000000000000000
χ874-4-44-24-222-22-42-44-21-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i000000000023−232i3−2i300000000000000000000−i3i300−33000000000000000
χ884-4-44-24-222-22-42-44-21-2-20-1-22212-2-12001-11-10000−3i3i00−3i3i−3i3i0000000000−2323−2i32i300000000000000000000i3−i3003−3000000000000000
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
χ9188-8-8-48-4-4-444-848-842-4-4024-44-2-44-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-4-44444-44422202-22-2-22-2-2-243−43-1-11100−232300−232333−3−30000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-44444-44422202-22-2-22-2-2-2−4343-1-1110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-8448-4-444-8-42-404-24-44-24-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4444-48-4-8-842-4-40-244-4-2442-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-8-8-4-48444-4-42044-2244-2-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-4-4-44442220-2-2-22-2-2-22200-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444-4-4-44442220-2-2-22-2-2-22200-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-84-4-8444-48-42-404244-4-2-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8844-84-4-4-4-4204-4-2-2-44244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-44444-4-42220-22-2-22-22-2-200-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-44444-4-42220-22-2-22-22-2-200-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000

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