Finite Group Databasebeta

← Group #13168519

Character table — Group #13168519

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212244446612121212121212121212446661212121212121212121212121212122444412121212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-11111-11-11111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-111-1-1111111-1-1-1-1-11111-111-1-1111111-11-1-1111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-11-11-1-111-1-111-1-1-1-11-1-1-1-1-1-111-1-1111-1-11
χ511111111111111111111111111111-1-11111111111111111111-11111-1-1111111-1-111111-11-111-1-111-1-111111-1-1-1-1-1-111-1-1-1-11-1-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-1-1-11-1-1111-1-1-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-111
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111-1-111-1-111-1-1111-1-1-11-111-1-1-1-111-1-11-11-11-1-1-1-111-1-111-11
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1111111111-11-1-1-111-1-1-1-1-1-111-111-1-111111111-1-1-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-111-1-111-111-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1-1-11-1-111111-1-1-1-11111-11-111-1-1-1-1-1-11-111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-111-1-1-1-1-1-11111-111-1-1-1-1-11111-1-111-11-111-1-1-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-111-1-1-111-1-111-1-1-1-1-1111
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-1-11-1111-1-1111111-1-1-111-1-1111111-1-1-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-111-1-1-1-1-1-1-1111-11-1-11111-1-1111-11-11-1-1-1-1111111-1-1
χ17222222-122-12-12-1222-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1220222200-1-1-1-1220022-1-1-10-102200-1-100-1-1-1-12000000-1-10000-1000
χ18222222-122-12-12-1222-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1220-2-22200-1-111-2-200-2-2-1-1-1010-2200-1-1001111-20000001100001000
χ19222222-122-12-12-1222-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2-2022-2-20011-1-12200-2-21110-102-2001100-1-1-1-1-20000001100001000
χ20222222-122-12-12-1222-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2-20-2-2-2-2001111-2-20022111010-2-200110011112000000-1-10000-1000
χ21222222-122-12-12-1222-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-21111112-202-2220011-1-1-2-200-2-2-1-1-10102-2001100-1-1112000000110000-1000
χ22222222-122-12-12-1222-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-21111112-20-2222001111220022-1-1-10-10-2-200110011-1-1-2000000-1-100001000
χ23222222-122-12-12-1222-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-2111111-2202-2-2-200-1-1-1-1-2-200221110102200-1-100-1-111-2000000-1-100001000
χ24222222-122-12-12-1222-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-2111111-220-22-2-200-1-1112200-2-21110-10-2200-1-10011-1-12000000110000-1000
χ2522222-12-122-12222-1-12-12-122-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-122200-1-122220000-1-1002-1-1-1020-1-1-1-1-1-1-10000002200000-1-10000-10
χ2622222-12-122-12222-1-12-12-122-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-2-22001122-2-20000-1-100-211-10201-1-111-1-1000000-2-20000011000010
χ2722222-12-122-12222-1-12-12-122-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-122-200-1-1-2-222000011002-1-110-20-111-1-111000000-2-20000011000010
χ2822222-12-122-12222-1-12-12-122-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-20011-2-2-2-200001100-21110-2011111110000002200000-1-10000-10
χ2922222-12-122-12222-1-12-1-2-122-1-1-1-1-1222-1-1-1-11-2-21111-2-211112-2-200-1-122-2-20000-1-1002-1-110-201-1-111110000002-200000-1-1000010
χ3022222-12-122-12222-1-12-1-2-122-1-1-1-1-1222-1-1-1-11-2-21111-2-21111-22-2001122220000-1-100-21110-20-1-1-1-1-111000000-2200000110000-10
χ3122222-12-122-12222-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-211112-2200-1-1-2-2-2-2000011002-1-1-102011111-1-1000000-2200000110000-10
χ3222222-12-122-12222-1-12-1-2-122-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-21111-2220011-2-22200001100-211-1020-111-1-1-1-10000002-200000-1-1000010
χ332222-1222-1222-12-12-1-122-1-1-122-12-1-122-1-1-1-122-122-1-1-1-1-1-1-1-10022200-1-10022-1-1220000022-1-10-1-100-1-1-1-1-1-102002-1-10000000-100
χ342222-1222-1222-12-12-1-122-1-1-122-12-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1002-2-200-1-100-2-21122000002-2-110-1-100-1-111110-200-2110000000100
χ352222-1222-1222-12-12-1-122-1-1-122-12-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-100-22200110022-1-1-2-200000-221-10110011-1-1-1-10-200-2110000000100
χ362222-1222-1222-12-12-1-122-1-1-122-12-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-100-2-2-2001100-2-211-2-200000-2-2110110011111102002-1-10000000-100
χ372222-1222-1222-12-12-1-12-2-1-1-122-12-1-122-1-1-1-1-2-21-2-21111111100-22-200-1-10022112200000-2-21-10-1-10011-1-1110-2002110000000-100
χ382222-1222-1222-12-12-1-12-2-1-1-122-12-1-122-1-1-1-1-2-21-2-21111111100-2-2200-1-100-2-2-1-12200000-22110-1-1001111-1-10200-2-1-10000000100
χ392222-1222-1222-12-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-2-21-2-2111111110022-20011002211-2-2000002-2-1-101100-1-1-1-1110200-2-1-10000000100
χ402222-1222-1222-12-12-1-12-2-1-1-122-12-1-1-2-2-1-1-1-1-2-21-2-211111111002-22001100-2-2-1-1-2-20000022-1101100-1-111-1-10-2002110000000-100
χ412-22-2222-222-2-2-2-2-222220-22-2-2-222-2-22-222-2-2000000000000000000002-20000002-22i−2i000000002-20000000000000002i−2i002i−2i0000
χ422-22-2222-222-2-2-2-2-222220-22-2-2-222-2-22-222-2-2000000000000000000002-20000002-2−2i2i000000002-2000000000000000−2i2i00−2i2i0000
χ432-22-2222-222-2-2-2-2-222220-22-2-2-222-2-2-2222-2-200000000000000000000-22000000-222i−2i00000000-220000000000000002i−2i00−2i2i0000
χ442-22-2222-222-2-2-2-2-222220-22-2-2-222-2-2-2222-2-200000000000000000000-22000000-22−2i2i00000000-22000000000000000−2i2i002i−2i0000
χ4544444-2-2-24-2-2-24-24-2-2-214-2-2-211-21-2-2001111-2-2411-2-2-2-2111144000-2-200-2-200000000-2110000-2001100000000000000000000000
χ4644444-2-2-24-2-2-24-24-2-2-214-2-2-211-21-2-2001111-2-2411-2-2-2-21111-4-4000220022000000002-1-10000200-1-100000000000000000000000
χ4744444-2-2-24-2-2-24-24-2-2-21-4-2-2-211-21-2-200111122-4-1-12222-1-1-1-14-4000-2-2002200000000-2110000200-1-100000000000000000000000
χ4844444-2-2-24-2-2-24-24-2-2-21-4-2-2-211-21-2-200111122-4-1-12222-1-1-1-1-440002200-2-2000000002-1-10000-2001100000000000000000000000
χ494444-24-24-2-24-2-2-2-24-21-24-211-2-2-2-2-210011114-2-2-2-2-2-211111100044000000-2-2-2-200000000-20-20000000111100000000000000000
χ504444-24-24-2-24-2-2-2-24-21-24-211-2-2-2-2-210011114-2-2-2-2-2-2111111000-4-40000002222000000002020000000-1-1-1-100000000000000000
χ514444-24-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-21001111-4222222-1-1-1-1-1-10004-4000000-2-2220000000020-2000000011-1-100000000000000000
χ524444-24-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-21001111-4222222-1-1-1-1-1-1000-4400000022-2-200000000-2020000000-1-11100000000000000000
χ534444-2-24-2-24-24-24-2-21-2-241-2-2-2-21-21-2441111-24-2-2-211-2-211110040000-2-2000000-2-200000-20-200110011000000000000000000000
χ544444-2-24-2-24-24-24-2-21-2-241-2-2-2-21-21-2-4-41111-24-2-2-211-2-2111100-4000022000000220000020200-1-100-1-1000000000000000000000
χ554444-2-24-2-24-24-24-2-21-2-2-41-2-2-2-21-21-24411112-4222-1-122-1-1-1-100-40000-2-2000000-2-200000202001100-1-1000000000000000000000
χ564444-2-24-2-24-24-24-2-21-2-2-41-2-2-2-21-21-2-4-411112-4222-1-122-1-1-1-10040000220000002200000-20-200-1-10011000000000000000000000
χ5744-4-44444-4-4-4-444-4-444404-444-4-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-42-424-2-4-44-2-2042-2-22-42-4200-22-22000000000000000000000023−2300000000000000000023−2300000000000000000000000
χ5944-4-444-24-42-424-2-4-44-2-2042-2-22-42-4200-22-220000000000000000000000−2323000000000000000000−232300000000000000000000000
χ6044-4-44-24-2-4-42-444-42-24-20-2-44-22222-400-22-22000000000000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ6144-4-44-24-2-4-42-444-42-24-20-2-44-22222-400-22-220000000000000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ6244-4-44-2-2-2-42224-2-42-2-210-22-21-12-122001-11-10003i−3i00003i3i−3i−3i00000−2i32i30023−23000000000i3−i30000000−3300000000000000000000000
χ6344-4-44-2-2-2-42224-2-42-2-210-22-21-12-122001-11-10003i−3i00003i3i−3i−3i000002i3−2i300−2323000000000−i3i300000003−300000000000000000000000
χ6444-4-44-2-2-2-42224-2-42-2-210-22-21-12-122001-11-1000−3i3i0000−3i−3i3i3i00000−2i32i300−2323000000000i3−i300000003−300000000000000000000000
χ6544-4-44-2-2-2-42224-2-42-2-210-22-21-12-122001-11-1000−3i3i0000−3i−3i3i3i000002i3−2i30023−23000000000−i3i30000000−3300000000000000000000000
χ6644-4-4-24442-4-4-4-242-4-2-240-22-24-42-42200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ6744-4-4-24442-4-4-4-242-4-2-240-22-24-42-42200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ684-44-444-2-44-2-42-42-444-2-20-4-22224-2-4200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ694-44-444-2-44-2-42-42-444-2-20-4-22224-2-4200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ704-44-44-242442-4-4-4-4-2-24-2024-422-2-22-44-4-2-222000000000000000000004-4000000-220000000000-220000000000000000000000000
χ714-44-44-242442-4-4-4-4-2-24-2024-422-2-22-4-44-2-22200000000000000000000-440000002-200000000002-20000000000000000000000000
χ724-44-4-244-4-24-4-42-424-2-2402-22-4-4-24224-4-2-22200000000000000000000-220000004-40000000000-220000000000000000000000000
χ734-44-4-244-4-24-4-42-424-2-2402-22-4-4-2422-44-2-222000000000000000000002-2000000-4400000000002-20000000000000000000000000
χ744-44-4-2-242-242-42-42-21-2-20-1-22221-2-124-411-1-1000003i−3i003i−3i3i−3i0000000-22000000-2200000000001-1003i−3i000000000000000000000
χ754-44-4-2-242-242-42-42-21-2-20-1-22221-2-124-411-1-100000−3i3i00−3i3i−3i3i0000000-22000000-2200000000001-100−3i3i000000000000000000000
χ764-44-4-2-242-242-42-42-21-2-20-1-22221-2-12-4411-1-1000003i−3i003i−3i3i−3i00000002-20000002-20000000000-1100−3i3i000000000000000000000
χ774-44-4-2-242-242-42-42-21-2-20-1-22221-2-12-4411-1-100000−3i3i00−3i3i−3i3i00000002-20000002-20000000000-11003i−3i000000000000000000000
χ784-4-44444-4-4-444-4-44-44440-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-424-2-424-44-2-20-4222-2-424-200-222-2000000000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000
χ804-4-4444-2-4-424-2-424-44-2-20-4222-2-424-200-222-20000000000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000
χ814-4-444-242-4-4-24-4-442-24-202-4-42-222-2400-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ824-4-444-242-4-4-24-4-442-24-202-4-42-222-2400-222-200000000000000000000000000000000000000000000000000000000000−2323000000
χ834-4-44-244-42-4442-4-2-4-2-240222-442-4-2-200-222-200000000000000000000000000−2i32i300000000000000000000−2i32i300000000000000000
χ844-4-44-244-42-4442-4-2-4-2-240222-442-4-2-200-222-2000000000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000
χ854-4-44-24-2-4224-222-2-4-21-202-1-12-222-21001-1-1100000003-33-3-3300000000000−2i32i3−2i32i3000000000000000000i3−i3i3−i300000000000000000
χ864-4-44-24-2-4224-222-2-4-21-202-1-12-222-21001-1-1100000003-33-3-33000000000002i3−2i32i3−2i3000000000000000000−i3i3−i3i300000000000000000
χ874-4-44-24-2-4224-222-2-4-21-202-1-12-222-21001-1-110000000-33-333-300000000000−2i32i32i3−2i3000000000000000000i3−i3−i3i300000000000000000
χ884-4-44-24-2-4224-222-2-4-21-202-1-12-222-21001-1-110000000-33-333-3000000000002i3−2i3−2i32i3000000000000000000−i3i3i3−i300000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4222822222222200-1-1-1-1-4-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222200-1-1-1-1444-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4844-84-4-44-8-42-40-4-22-44444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-44-84-8-48442-4-4024-4-44-24-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44444-4-44422202-222-2-2-2-2-200-11-110006i−6i0000−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44444-4-44422202-222-2-2-2-2-200-11-11000−6i6i00003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-448-444-84-8-4-4-4204-44-2-2-42440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-8-4-4-844448-42-4042-244-4-44-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4-444444-42220-22-2-2-222-2-200-1-111000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4-444444-42220-22-2-2-222-2-200-1-11100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-44-84-4-4-8484-4-420444-224-2-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8-484-8-442-4-40-2444-4-242-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-4-444-442220-2-2-2-22-2-22200-111-100000006-6-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-4-444-442220-2-2-2-22-2-22200-111-10000000-663-3-33000000000000000000000000000000000000000000000000000000

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