Finite Group Databasebeta

← Group #13168541

Character table — Group #13168541

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212443666121212121212121212121212444441212121212121212441212121212121212121212121212121212121212224446666121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111-1-111-111111111-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-11111111-1-111-1-11-1-111-1111111-1-1-1-11111-1-1-111-1-1-1-111-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1111-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-1-1-1111111-111111-11-1-1-1-111111111-11-1-1-1-1-111-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111111-11-11-1-1-1-111-1-111-1-111-1-11-1-1-1111-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1-11-1-11-1-1111-1-111-1-1-1-11111-11-11111-1-1-1-1-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-111-11-1-111-1-1-1-11111-1-1-111-11-1-11111-1-1-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-11-111-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1111111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-111111111-11-1-11-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-1-1-111-1-11-111-1-11111-1-1-1-111-111-11-1-11111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-11-111-111-1-1-111-1-11111-1-111-11-11111-1-1-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111-11-11111-1-111-1-111-1-1111-1-1-1111-1-11111-1-1-1-11
χ17222222-12-122-12-1222-1-122-1-1-1-122-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-12202200002222220-1-1-1-12020000-1-1-1-1-1-1-1-10200000-1-100-1-100000
χ18222222-12-122-12-1222-1-122-1-1-1-122-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1220-2-2000022-2-2-2-20-1-11120-20000-1-1-1-111110-20000011001100000
χ19222222-12-122-12-1222-1-122-1-1-1-122-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20220000-2-222-2-2011-1-1-20200001111-1-1-1-10-20000011001100000
χ20222222-12-122-12-1222-1-122-1-1-1-122-1-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-20-2-20000-2-2-2-22201111-20-20000111111110200000-1-100-1-100000
χ21222222-12-122-12-1222-1-1-22-1-1-1-122-1-11100-1-1-1-1-2-211-2-21111112-202-200002222220-11-11-20-20000-1-111-1-1110-2000001100-1-100000
χ22222222-12-122-12-1222-1-1-22-1-1-1-122-1-11100-1-1-1-1-2-211-2-21111112-20-22000022-2-2-2-20-111-1-2020000-1-11111-1-10200000-1-1001100000
χ23222222-12-122-12-1222-1-1-22-1-1-1-122-1-11100-1-1-1-1-2-211-2-2111111-2202-20000-2-222-2-201-1-1120-2000011-1-1-1-1110200000-1-1001100000
χ24222222-12-122-12-1222-1-1-22-1-1-1-122-1-11100-1-1-1-1-2-211-2-2111111-220-220000-2-2-2-22201-11-1202000011-1-111-1-10-2000001100-1-100000
χ2522222-12-122-1222-12-12-12-122-1-1-1-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12220022-1-1-1-10000-12200-120-1-1-1-1-1-1-1-1000020200-1-100000000-100
χ2622222-12-122-1222-12-12-12-122-1-1-1-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-220022-1-1110000-1-2-200120-1-1-1-111110000-20-2001100000000100
χ2722222-12-122-1222-12-12-12-122-1-1-1-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-122-200-2-211-1-1000012200-1-201111-1-1-1-10000-20-2001100000000100
χ2822222-12-122-1222-12-12-12-122-1-1-1-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-200-2-2111100001-2-2001-2011111111000020200-1-100000000-100
χ2922222-12-122-1222-12-12-1-2-122-1-1-1-1-12-2-222-1-1-1-11-21111-2-211112-2-20022-1-1-1-1000012-2001-20-1-111-1-111000020-200-1-100000000100
χ3022222-12-122-1222-12-12-1-2-122-1-1-1-1-12-2-222-1-1-1-11-21111-2-21111-22-20022-1-11100001-2200-1-20-1-11111-1-10000-202001100000000-100
χ3122222-12-122-1222-12-12-1-2-122-1-1-1-1-12-2-2-2-2-1-1-1-11-21111-2-211112-2200-2-211-1-10000-12-20012011-1-1-1-1110000-202001100000000-100
χ3222222-12-122-1222-12-12-1-2-122-1-1-1-1-12-2-2-2-2-1-1-1-11-21111-2-21111-22200-2-211110000-1-2200-12011-1-111-1-1000020-200-1-100000000100
χ332222-12222-122-122-1-1-122-1-1-122-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-100222-1-12200-1-100200220-1-1-1-1-1-10000-1-1-1-1000220000-1-100000-10
χ342222-12222-122-122-1-1-122-1-1-122-1-12-12222-1-1-1-12-122-1-1-1-1-1-1-1-1002-2-2-1-122001100200-2-20-11-1-1-1-100001111000-2-20000110000010
χ352222-12222-122-122-1-1-122-1-1-122-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-22211-2-200-1-100-2002201-111110000-1-1-1-1000-2-20000110000010
χ362222-12222-122-122-1-1-122-1-1-122-1-12-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100-2-2-211-2-2001100-200-2-2011111100001111000220000-1-100000-10
χ372222-12222-122-122-1-1-12-2-1-1-122-1-12-1-2-222-1-1-1-1-21-2-21111111100-22-2-1-12200-1-100-2002-2011-1-1110000-1-111000-220000-1-10000010
χ382222-12222-122-122-1-1-12-2-1-1-122-1-12-1-2-222-1-1-1-1-21-2-21111111100-2-22-1-122001100-200-2201-1-1-111000011-1-10002-200001100000-10
χ392222-12222-122-122-1-1-12-2-1-1-122-1-12-1-2-2-2-2-1-1-1-1-21-2-2111111110022-211-2-200-1-1002002-20-1111-1-10000-1-1110002-200001100000-10
χ402222-12222-122-122-1-1-12-2-1-1-122-1-12-1-2-2-2-2-1-1-1-1-21-2-211111111002-2211-2-2001100200-220-1-111-1-1000011-1-1000-220000-1-10000010
χ4122-2-2222-2-22-22-2-22-22220-22-2-2-22-22-2002-222-2-2000000000000000002-22-200002i−2i000000002-20000000000000000000002i−2i2i−2i000
χ4222-2-2222-2-22-22-2-22-22220-22-2-2-22-22-2002-222-2-2000000000000000002-22-20000−2i2i000000002-2000000000000000000000−2i2i−2i2i000
χ4322-2-2222-2-22-22-2-22-22220-22-2-2-22-22-200-2222-2-200000000000000000-22-2200002i−2i00000000-220000000000000000000002i−2i−2i2i000
χ4422-2-2222-2-22-22-2-22-22220-22-2-2-22-22-200-2222-2-200000000000000000-22-220000−2i2i00000000-22000000000000000000000−2i2i2i−2i000
χ4544444-2-2-2-24-2-24-2-24-2-214-2-2-211-2-21-2-2-2001111-2411-2-2-2-21111440000000-2-200000-2-200-200000011110000000000000000000000
χ4644444-2-2-2-24-2-24-2-24-2-214-2-2-211-2-21-2-2-2001111-2411-2-2-2-21111-4-40000000220000022002000000-1-1-1-10000000000000000000000
χ4744444-2-2-2-24-2-24-2-24-2-21-4-2-2-211-2-21-2220011112-4-1-12222-1-1-1-14-40000000-2-200000-2200200000011-1-10000000000000000000000
χ4844444-2-2-2-24-2-24-2-24-2-21-4-2-2-211-2-21-2220011112-4-1-12222-1-1-1-1-44000000022000002-200-2000000-1-1110000000000000000000000
χ494444-24-24-2-24-2-2-24-2-21-24-211-2-2-2-2-21-2-20011114-2-2-2-2-211111100044000000-2-200000-2-200-2000000001111000000000000000000
χ504444-24-24-2-24-2-2-24-2-21-24-211-2-2-2-2-21-2-20011114-2-2-2-2-2111111000-4-400000022000002200200000000-1-1-1-1000000000000000000
χ514444-24-24-2-24-2-2-24-2-21-2-4-211-2-2-2-2-2122001111-422222-1-1-1-1-1-10004-4000000-2-200000-220020000000011-1-1000000000000000000
χ524444-24-24-2-24-2-2-24-2-21-2-4-211-2-2-2-2-2122001111-422222-1-1-1-1-1-1000-4400000022000002-200-200000000-1-111000000000000000000
χ534444-2-24-24-2-24-24-2-21-2-241-2-2-2-211-2-244441111-2-2-2-211-2-2111100400-2-2-2-2000000-200000-20111100000000000000000000000000
χ544444-2-24-24-2-24-24-2-21-2-241-2-2-2-211-2-244-4-41111-2-2-2-211-2-2111100-400222200000020000020-1-1-1-100000000000000000000000000
χ554444-2-24-24-2-24-24-2-21-2-2-41-2-2-2-211-2-2-4-44411112222-1-122-1-1-1-100-400-2-2-2-20000002000002011-1-100000000000000000000000000
χ564444-2-24-24-2-24-24-2-21-2-2-41-2-2-2-211-2-2-4-4-4-411112222-1-122-1-1-1-1004002222000000-200000-20-1-11100000000000000000000000000
χ5744-4-444-2-424-4-2-424-44-2-20-4-22224-4-220000-2-22200000000000000000000000004i−4i0000000000000000000000000000000−2i2i00000
χ5844-4-444-2-424-4-2-424-44-2-20-4-22224-4-220000-2-2220000000000000000000000000−4i4i00000000000000000000000000000002i−2i00000
χ5944-4-44-242-4424-4-4-2-4-24-2024-422-22-2-4004-4-2-222000000000000000004-4-2200000000000000-220000000000000000000000000000
χ6044-4-44-242-4424-4-4-2-4-24-2024-422-22-2-400-44-2-22200000000000000000-442-2000000000000002-20000000000000000000000000000
χ6144-4-4-244-4-4-2-442-442-2-2402-22-4-4-2242004-4-2-22200000000000000000-224-400000000000000-220000000000000000000000000000
χ6244-4-4-244-4-4-2-442-442-2-2402-22-4-4-224200-44-2-222000000000000000002-2-44000000000000002-20000000000000000000000000000
χ6344-4-4-2-242-4-2242-4-221-2-20-1-22221-1-22004-411-1-100003i−3i003i3i−3i−3i00000-22-22000000000000001-13i−3i00000000000000000000000000
χ6444-4-4-2-242-4-2242-4-221-2-20-1-22221-1-22004-411-1-10000−3i3i00−3i−3i3i3i00000-22-22000000000000001-1−3i3i00000000000000000000000000
χ6544-4-4-2-242-4-2242-4-221-2-20-1-22221-1-2200-4411-1-100003i−3i003i3i−3i−3i000002-22-200000000000000-11−3i3i00000000000000000000000000
χ6644-4-4-2-242-4-2242-4-221-2-20-1-22221-1-2200-4411-1-10000−3i3i00−3i−3i3i3i000002-22-200000000000000-113i−3i00000000000000000000000000
χ674-44-4444-4-4-44-4-44-444440-4-4-4-44-44-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-42-442-4-2-444-2-20-4222-2-442-2−2i32i300-222-200−2i32i300−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ694-44-444-2-42-442-4-2-444-2-20-4222-2-442-22i3−2i300-222-2002i3−2i3002i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ704-44-44-242-4-4-2-4-4424-24-202-4-42-22-2240000-222-200000000000000000000023−23000000000000000023−23000000000000000000000000
χ714-44-44-242-4-4-2-4-4424-24-202-4-42-22-2240000-222-2000000000000000000000−23230000000000000000−2323000000000000000000000000
χ724-44-44-2-222-4-22-4-224-2-210222-112-2-1-2−2i32i3001-1-1100i3−i300−2i32i3i3−i3i3−i300000000023−230000000000000000−333i−3i0000000000000000000000
χ734-44-44-2-222-4-22-4-224-2-210222-112-2-1-2−2i32i3001-1-1100i3−i300−2i32i3i3−i3i3−i3000000000−232300000000000000003−3−3i3i0000000000000000000000
χ744-44-44-2-222-4-22-4-224-2-210222-112-2-1-22i3−2i3001-1-1100−i3i3002i3−2i3−i3i3−i3i300000000023−230000000000000000−33−3i3i0000000000000000000000
χ754-44-44-2-222-4-22-4-224-2-210222-112-2-1-22i3−2i3001-1-1100−i3i3002i3−2i3−i3i3−i3i3000000000−232300000000000000003−33i−3i0000000000000000000000
χ764-44-4-244-4-424-424-4-2-2-240222-442-2-4-20000-222-200000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000
χ774-44-4-244-4-424-424-4-2-2-240222-442-2-4-20000-222-2000000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000
χ784-44-4-24-2-422422-2-4-2-21-202-1-12-22-221−2i32i3001-1-1100−2i32i300i3−i3i3−i3i3−i300000000000−2i32i3000000000000000000i3−i33-3000000000000000000
χ794-44-4-24-2-422422-2-4-2-21-202-1-12-22-221−2i32i3001-1-1100−2i32i300i3−i3i3−i3i3−i3000000000002i3−2i3000000000000000000−i3i3-33000000000000000000
χ804-44-4-24-2-422422-2-4-2-21-202-1-12-22-2212i3−2i3001-1-11002i3−2i300−i3i3−i3i3−i3i300000000000−2i32i3000000000000000000i3−i3-33000000000000000000
χ814-44-4-24-2-422422-2-4-2-21-202-1-12-22-2212i3−2i3001-1-11002i3−2i300−i3i3−i3i3−i3i3000000000002i3−2i3000000000000000000−i3i33-3000000000000000000
χ824-4-4444444-4-4-44-4-4-444404-444-4-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-24-2-4-4242-4-44-2-2042-2-22-4-4220000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ844-4-4444-24-2-4-4242-4-44-2-2042-2-22-4-4220000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ854-4-444-24-24-42-44-42-4-24-20-2-44-22222-40000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ864-4-444-24-24-42-44-42-4-24-20-2-44-22222-40000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ874-4-44-244442-4-4-2-4-42-2-240-22-24-422-420000-22-2200000000000000000000000000000000000000000000000000000000−2i32i30000000
χ884-4-44-244442-4-4-2-4-42-2-240-22-24-422-420000-22-22000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-44484-4-84-4-8-4-4204-44-2-2-4424000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-84-4-8-44484-42-4042-244-44-4-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-44-444-442220-22-2-2-22-22-20000-1-11100006i−6i00−3i−3i3i3i00000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-44-444-442220-22-2-2-22-22-20000-1-1110000−6i6i003i3i−3i−3i00000000000000000000000000000000000000000000000000000
χ958-88-8-4-484-84-4-8484-42-4-40-2444-4-224-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4444-444-44-42220-2-2-2-22-22-22−4i34i300-111-1002i3−2i3002i3−2i3−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-444-44-42220-2-2-2-22-22-224i3−4i300-111-100−2i32i300−2i32i3i3−i3i3−i300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-4-4-844844-8-4-420-44-42-244-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-48-44-84-44-84-42-40-4-22-44444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-4844-8-4-8442-4-4024-4-44-2-24400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4-4444-444422202-222-2-2-2-2-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4-4444-444422202-222-2-2-2-2-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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