Finite Group Databasebeta

← Group #13169277

Character table — Group #13169277

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212444441212121212121212121212124412121212121212121212121212121212121222444661212121222612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111111-1-111-1-1-1-1111-11-111111111-1-1-1-111-1-1-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1111-1-1-111-1-1111111-1-11-111-1111-1-111-1-11111-1-11-11-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-1-1-111-1-1-1-111-1-1111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-1111111111111111111-111111-1-11111-1-11111-11-1111-1-111-1-1111111-1-1-11-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-1-1111-1-111-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-1-1-1-1-11-11-1-111-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-11111-1-1-1-1-11-1-1-11-1-11111-1-111-1-11-111-1-1-111-1-1-1-11-111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111-1-1-1-1111111-11-11-1-1-1-11111-1-1-1-1111-1-1-11-1-1-1-1111111-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-111-1-111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-11111-1-111-11-11111-1-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-1-1111-1-111111-1-1-1-111-1-1-11-11111-1-1-1-111-111-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-111-1-1111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-11-1-1-11-1-1-1-111-1-111-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-111-1-11-1111-111-1-1-1-111-1-1111-111-1-1-111-1-1111-11-1
χ17222222-12-1-1-1222222-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-12200222-1-1-1-100220000-1-12020-1-1-1-1-1-1-1-1000022000-1-1000000-1000
χ18222222-12-1-1-1222222-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2200-2-2-2-1-11100220000-1120-20-1-111-1-1110000-2-2000110000001000
χ19222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-12-20022211-1-100-2-200001-1-202011-1-111-1-10000-2-2000110000001000
χ20222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-2111100-2-2000011-20-2011111111000022000-1-1000000-1000
χ21222222-12-1-1-1222222-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-2-2-2111111112-200-222-1-111002200001-1-20-2011-1-1-1-11100002-200011000000-1000
χ22222222-12-1-1-1222222-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-2-2-211111111-2-2002-2-2-1-1-1-10022000011-20201111-1-1-1-10000-22000-1-10000001000
χ23222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-2-2-2111111112200-222111100-2-20000-1-120-20-1-1-1-111110000-22000-1-10000001000
χ24222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-2-2-211111111-22002-2-211-1-100-2-20000-112020-1-11111-1-100002-200011000000-1000
χ2522222-122222-1-12-12-12-12-12-1-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-102220002200-1-1-1-1220020-1-102-1-100-1-100-1-1-1-10020200-1-100000-100
χ2622222-122222-1-12-12-12-12-12-1-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-102-2-2000220011-1-1-2-20020-110-2-1-100-1-100111100-20-2001100000100
χ2722222-122222-1-12-12-12-12-12-1-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-10-222000-2-200-1-1112200-201-10211001100-1-1-1-100-20-2001100000100
χ2822222-122222-1-12-12-12-12-12-1-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-10-2-2-2000-2-2001111-2-200-20110-21100110011110020200-1-100000-100
χ2922222-122222-1-12-12-12-1-2-12-1-12-12-1-122-1-1-1-1-2-2111-2-21111110-22-20002200-1-1-1-1-2-200-2011021100-1-100-1-1110020-200-1-100000100
χ3022222-122222-1-12-12-12-1-2-12-1-12-12-1-122-1-1-1-1-2-2111-2-21111110-2-22000220011-1-12200-201-10-21100-1-10011-1-100-202001100000-100
χ3122222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2-1-1-1-1-2-2111-2-2111111022-2000-2-200-1-111-2-20020-1102-1-1001100-1-11100-202001100000-100
χ3222222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2-1-1-1-1-2-2111-2-211111102-22000-2-2001111220020-1-10-2-1-100110011-1-10020-200-1-100000100
χ332222-122-122222-12-1-1-122-1-12-1-12-12-100-1-1-1-12-12-1-1-1-122-1-1-1-120222-1-100222200-1-1220202-1-100-1-100-1-1-1-1-1-1000200000-1-10000-10
χ342222-122-122222-12-1-1-122-1-12-1-12-12-100-1-1-1-12-12-1-1-1-122-1-1-1-120-2-22-1-10022-2-20011-2-2020-2-1100-1-100-1-11111000-20000011000010
χ352222-122-122222-12-1-1-122-1-12-1-12-12-100-1-1-1-12-12-1-1-1-122-1-1-1-1-2022-21100-2-22200-1-1-2-20-2021-100110011-1-1-1-1000-20000011000010
χ362222-122-122222-12-1-1-122-1-12-1-12-12-100-1-1-1-12-12-1-1-1-122-1-1-1-1-20-2-2-21100-2-2-2-20011220-20-211001100111111000200000-1-10000-10
χ372222-122-122222-12-1-1-12-2-1-12-1-12-12-100-1-1-1-1-21-21111-2-21111202-2-2-1-100-2-2220011-2-2020-21-100-1-10011-1-111000200000110000-10
χ382222-122-122222-12-1-1-12-2-1-12-1-12-12-100-1-1-1-1-21-21111-2-2111120-22-2-1-100-2-2-2-200-1-12202021100-1-1001111-1-1000-200000-1-1000010
χ392222-122-122222-12-1-1-12-2-1-12-1-12-12-100-1-1-1-1-21-21111-2-21111-202-22110022220011220-20-2-1-1001100-1-1-1-111000-200000-1-1000010
χ402222-122-122222-12-1-1-12-2-1-12-1-12-12-100-1-1-1-1-21-21111-2-21111-20-222110022-2-200-1-1-2-20-202-11001100-1-111-1-1000200000110000-10
χ412-22-2222-22-2-22-2-2-222220-22-2-2-22-2-222i−2i22-2-2000000000000000000002i−2i00002i−2i002i−2i00000000002i−2i0000000000000002i−2i2-20000
χ422-22-2222-22-2-22-2-2-222220-22-2-2-22-2-222i−2i22-2-2000000000000000000002i−2i00002i−2i00−2i2i00000000002i−2i000000000000000−2i2i-220000
χ432-22-2222-22-2-22-2-2-222220-22-2-2-22-2-22−2i2i22-2-200000000000000000000−2i2i0000−2i2i002i−2i0000000000−2i2i0000000000000002i−2i-220000
χ442-22-2222-22-2-22-2-2-222220-22-2-2-22-2-22−2i2i22-2-200000000000000000000−2i2i0000−2i2i00−2i2i0000000000−2i2i000000000000000−2i2i2-20000
χ4544444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-2441111-24-2-2-2-2-21111110400000-2-20000-2-20000-20-200011001100000000000000000000000
χ4644444-2-24-2-2-2-2-24-24-2-214-2-21-2-21-21-2-4-41111-24-2-2-2-2-21111110-400000220000220000202000-1-100-1-100000000000000000000000
χ4744444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-24411112-422222-1-1-1-1-1-10-400000-2-20000-2-20000202000-1-1001100000000000000000000000
χ4844444-2-24-2-2-2-2-24-24-2-21-4-2-21-2-21-21-2-4-411112-422222-1-1-1-1-1-10400000220000220000-20-20001100-1-100000000000000000000000
χ494444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2001111-2-24-2-211-2-2111140004-2-200-2-2000000000-200-2000110011000000000000000000000
χ504444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2001111-2-24-2-211-2-21111-4000-42200220000000002002000-1-100-1-1000000000000000000000
χ514444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-200111122-422-1-122-1-1-1-14000-4-2-20022000000000-20020001100-1-1000000000000000000000
χ524444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-200111122-422-1-122-1-1-1-1-400042200-2-2000000000200-2000-1-10011000000000000000000000
χ534444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-210011114-2-211-2-2-2-2111100440000000-2-200-2-200000-20-200000000111100000000000000000
χ544444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-210011114-2-211-2-2-2-2111100-4-400000002200220000020200000000-1-1-1-100000000000000000
χ554444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-21001111-422-1-12222-1-1-1-1004-40000000-2-200220000020-20000000011-1-100000000000000000
χ564444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-21001111-422-1-12222-1-1-1-100-4400000002200-2-200000-20200000000-1-11100000000000000000
χ5744-4-44444-44-4-44-4-4-444404-44-44-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-242-22-44-4-4-44-2-2042-2-4-2222-400-22-22000000000000000000000023−230000000000000000000023−23000000000000000000000
χ5944-4-444-242-22-44-4-4-44-2-2042-2-4-2222-400-22-220000000000000000000000−232300000000000000000000−2323000000000000000000000
χ6044-4-44-244-44-42-2-42-4-24-20-2-4-2242-42200-22-22000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ6144-4-44-244-44-42-2-42-4-24-20-2-4-2242-42200-22-220000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ6244-4-4-244-2-44-4-442-42-2-240-2242-2-42-4200-22-22000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000000000
χ6344-4-4-244-2-44-4-442-42-2-240-2242-2-42-4200-22-220000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000000000
χ6444-4-4-24-2-22-22-442-42-21-20-2-1-2212-122001-11-1000003i−3i003i3i−3i−3i00000−2i32i30023−230000000000000000i3−i300−33000000000000000000000
χ6544-4-4-24-2-22-22-442-42-21-20-2-1-2212-122001-11-1000003i−3i003i3i−3i−3i000002i3−2i300−23230000000000000000−i3i3003−3000000000000000000000
χ6644-4-4-24-2-22-22-442-42-21-20-2-1-2212-122001-11-100000−3i3i00−3i−3i3i3i00000−2i32i300−23230000000000000000i3−i3003−3000000000000000000000
χ6744-4-4-24-2-22-22-442-42-21-20-2-1-2212-122001-11-100000−3i3i00−3i−3i3i3i000002i3−2i30023−230000000000000000−i3i300−33000000000000000000000
χ684-44-444-2-4-2224-4-4-444-2-20-4-22-42-22244i−4i-2-22200000000000000000000−2i2i00004i−4i00000000000000−2i2i00000000000000000000000
χ694-44-444-2-4-2224-4-4-444-2-20-4-22-42-2224−4i4i-2-222000000000000000000002i−2i0000−4i4i000000000000002i−2i00000000000000000000000
χ704-44-44-24-44-4-4-22-424-24-202422-4-2-42-24i−4i-2-222000000000000000000004i−4i0000−2i2i00000000000000−2i2i00000000000000000000000
χ714-44-44-24-44-4-4-22-424-24-202422-4-2-42-2−4i4i-2-22200000000000000000000−4i4i00002i−2i000000000000002i−2i00000000000000000000000
χ724-44-44-2-2-4-222-22-424-2-2102-2-12212-1-24i−4i11-1-100000003i−3i3i−3i3i−3i0000000−2i2i0000−2i2i00000000003-300i−i00000000000000000000000
χ734-44-44-2-2-4-222-22-424-2-2102-2-12212-1-24i−4i11-1-10000000−3i3i−3i3i−3i3i0000000−2i2i0000−2i2i0000000000-3300i−i00000000000000000000000
χ744-44-44-2-2-4-222-22-424-2-2102-2-12212-1-2−4i4i11-1-100000003i−3i3i−3i3i−3i00000002i−2i00002i−2i0000000000-3300−ii00000000000000000000000
χ754-44-44-2-2-4-222-22-424-2-2102-2-12212-1-2−4i4i11-1-10000000−3i3i−3i3i−3i3i00000002i−2i00002i−2i00000000003-300−ii00000000000000000000000
χ764-44-4-24424-4-44-42-4-2-2-2402-2-42242-4-200-2-2220000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ774-44-4-24424-4-44-42-4-2-2-2402-2-42242-4-200-2-222000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ784-4-44444-4-4-44-4-444-44440-4-4-44-4-444-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-422-2-4-444-44-2-20-422422-2-2-400-222-20000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ804-4-4444-2-422-2-4-444-44-2-20-422422-2-2-400-222-200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ814-4-444-24-4-4-44224-2-4-24-202-42-2-424-2200-222-200000000000000000000000023−230000000000000000000023−230000000000000000000
χ824-4-444-24-4-4-44224-2-4-24-202-42-2-424-2200-222-2000000000000000000000000−232300000000000000000000−23230000000000000000000
χ834-4-44-2442-4-44-4-4-242-2-24022-4-22-4-24200-222-2000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ844-4-44-2442-4-44-4-4-242-2-24022-4-22-4-24200-222-20000000000000000000000000000−2323000000000000000000−232300000000000000000
χ854-4-44-2-242-4-4422-2-221-2-20-122122-2-2-1001-1-110003-300003-3-330000000000023−230023−230000000000000000−33−3300000000000000000
χ864-4-44-2-242-4-4422-2-221-2-20-122122-2-2-1001-1-110003-300003-3-3300000000000−232300−232300000000000000003−33−300000000000000000
χ874-4-44-2-242-4-4422-2-221-2-20-122122-2-2-1001-1-11000-330000-333-30000000000023−2300−23230000000000000000−333−300000000000000000
χ884-4-44-2-242-4-4422-2-221-2-20-122122-2-2-1001-1-11000-330000-333-300000000000−23230023−2300000000000000003−3−3300000000000000000
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
χ9188-8-88-4-484-444-4-84-8-4-420-4424-4-24-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4-88-84-44442-4-4024-4-2-4444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-444-444422202-22-22-2-2-2-200-11-11000006i−6i00−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-444-444422202-22-22-2-2-2-200-11-1100000−6i6i003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-44-4448-84-8-4-42-404244-2-4-24-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4848-8-8-4444-42-4-40-2-44-24-44420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-444-4444-42220-22-2-2-22-2-2200-1-11100000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-444-4444-42220-22-2-2-22-2-2200-1-1110000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844-4448-4-8-4-42044-2-44-2-424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-4444-4-8-8-484-42-404-24-4-242-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-442220-2-2-22-2-222-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-442220-2-2-22-2-222-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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