Finite Group Databasebeta

← Group #13168664

Character table — Group #13168664

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212443666121212121212121212121212244441212121212121212446666121212121212121212121212121212124444412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1111111-1-11111-11-11-111111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1111-11111-1-111-1-1-1-1-1-1111-11111-1-1111111-1-111-1-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-1-1-111-1-11111-1-1-1-1-11-1-1-1111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-11111111-1111-1-1-11111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-1-11-1-1-1-111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-11111-1-1-1-11-1-1-1-1-11111-1-11-11-1111-1-1-1-111-1-11-11
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1111111111-11-1-1-1-1-1-1-1-1-111111-1-11-1-1-111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-111-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-11-111-1-1-1-111-1-11111-11-11111-1-111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-1-1-1-11111-11-1-11111-1-111-1-1-1-1-11-11111-1-111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-111-111-1-1-1-1111111-1-1-1-11
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-111-1-1-1-1-11-1111111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-111111-1-1-1-1111-11-1111-1-1-1-111111-1-1
χ17222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-12220222002200222-1-1-1-102-1-1000-1-1-1-100-1-100002-1-1-1-1000000000
χ18222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-12-2-202-2-2002200-2-22-1-1-110-2-11000-1-11100110000-21111000000000
χ19222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2220-22200-2-200-2-2-2111-1021-100011-1-100-1-10000-21111000000000
χ20222222-122-122-1-1222-1-122-1-1-12-1-12-1-1-100-1-1-1-122-1-122-1-1-1-1-1-1-2-2-20-2-2-200-2-20022-211110-2110001111001100002-1-1-1-1000000000
χ21222222-122-122-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-211111122-20-22200-2-200-2-22-1-1-110-21-100011-1-1001100002-1-111000000000
χ22222222-122-122-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-21111112-220-2-2-200-2-200222-1-1-1-10211000111100-1-10000-211-1-1000000000
χ23222222-122-122-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-22-2022200220022-211110-2-1-1000-1-1-1-100110000-211-1-1000000000
χ24222222-122-122-1-1222-1-1-22-1-1-12-1-12-11100-1-1-1-1-2-211-2-2111111-2-2202-2-2002200-2-2-2111-102-11000-1-11100-1-100002-1-111000000000
χ2522222-122-12-1222-12-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12002200-1-1-1-12200-12-1-10-10202-1-1-1-100-1-100220000000-1-10000-100
χ2622222-122-12-1222-12-12-12-12-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-2002-200-1-11122001-2110-10-202-1-11100-1-100-2-20000000110000100
χ2722222-122-12-1222-12-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1200-220011-1-1-2-200-12-1-101020-211-1-1001100-2-20000000110000100
χ2822222-122-12-1222-12-12-12-12-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-200-2-2001111-2-2001-211010-20-21111001100220000000-1-10000-100
χ2922222-122-12-1222-12-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111200-2-200-1-1112200-12-1-1010-20-2111100-1-1002-20000000110000-100
χ3022222-122-12-1222-12-12-1-2-12-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-200-2200-1-1-1-122001-21101020-211-1-100-1-100-220000000-1-10000100
χ3122222-122-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-211112002-2001111-2-200-12-1-10-10-202-1-111001100-220000000-1-10000100
χ3222222-122-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111-200220011-1-1-2-2001-2110-10202-1-1-1-10011002-20000000110000-100
χ332222-122-1222-1222-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-102220-1-12200-1-100000022-102-1-1-100-1-1-1-1-1-100220000000-1-1000-10
χ342222-122-1222-1222-1-1-122-1-122-1-12-1-12222-1-1-1-12-122-1-1-1-1-1-1-1-10-2-220112200-1-1000000-2210-2-1-1-10011-1-11100-2-200000001100010
χ352222-122-1222-1222-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1022-20-1-1-2-200110000002-2-10211100-1-111-1-100-2-200000001100010
χ362222-122-1222-1222-1-1-122-1-122-1-12-1-122-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-2011-2-20011000000-2-210-21110011111100220000000-1-1000-10
χ372222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-21111111102-2-20-1-12200-1-1000000-2-210211100-1-1-1-111002-20000000-1-100010
χ382222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-222-1-1-1-1-21-2-2111111110-22-20112200-1-10000002-2-10-21110011-1-1-1-100-22000000011000-10
χ392222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-21111111102-220-1-1-2-20011000000-22102-1-1-100-1-1111100-22000000011000-10
χ402222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-2-2-2-1-1-1-1-21-2-2111111110-222011-2-2001100000022-10-2-1-1-1001111-1-1002-20000000-1-100010
χ412-2-22222-2-2-22-22-2-222220-22-2-22-22-2-2002i−2i22-2-200000000000000000002i−2i002i−2i2i−2i00000000000000002i−2i0000000002i−2i00002-2000
χ422-2-22222-2-2-22-22-2-222220-22-2-22-22-2-2002i−2i22-2-200000000000000000002i−2i002i−2i−2i2i00000000000000002i−2i000000000−2i2i0000-22000
χ432-2-22222-2-2-22-22-2-222220-22-2-22-22-2-200−2i2i22-2-20000000000000000000−2i2i00−2i2i2i−2i0000000000000000−2i2i0000000002i−2i0000-22000
χ442-2-22222-2-2-22-22-2-222220-22-2-22-22-2-200−2i2i22-2-20000000000000000000−2i2i00−2i2i−2i2i0000000000000000−2i2i000000000−2i2i00002-2000
χ4544444-2-24-2-2-24-2-2-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111400040000-2-20000-2-211000-2000011000000000000000000000000
χ4644444-2-24-2-2-24-2-2-24-2-214-2-211-2-21-2-2-2-2001111-2411-2-2-2-21111-4000-4000022000022-1-100020000-1-1000000000000000000000000
χ4744444-2-24-2-2-24-2-2-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-14000-40000220000-2-21100020000-1-1000000000000000000000000
χ4844444-2-24-2-2-24-2-2-24-2-21-4-2-211-2-21-2-2220011112-4-1-12222-1-1-1-1-400040000-2-2000022-1-1000-2000011000000000000000000000000
χ494444-24-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-211111104400-2-2000000000000-20-20-200000110011000000000000000000
χ504444-24-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-20011114-2-2-2-2-21111110-4-400220000000000002020200000-1-100-1-1000000000000000000
χ514444-24-2-24-24-2-2-24-2-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-104-400-2-20000000000002020-2000001100-1-1000000000000000000
χ524444-24-2-24-24-2-2-24-2-21-2-4-21-2-2-21-2-2122001111-422222-1-1-1-1-1-10-440022000000000000-20-20200000-1-10011000000000000000000
χ534444-2-24-2-24-2-244-2-21-2-241-2-2-21-2-21-244441111-2-2-2-211-2-211110004000-2-200-2-20000000-2000-21100001100000000000000000000
χ544444-2-24-2-24-2-244-2-21-2-241-2-2-21-2-21-244-4-41111-2-2-2-211-2-21111000-4000220022000000020002-1-10000-1-100000000000000000000
χ554444-2-24-2-24-2-244-2-21-2-2-41-2-2-21-2-21-2-4-44411112222-1-122-1-1-1-1000-4000-2-200-2-2000000020002-1-100001100000000000000000000
χ564444-2-24-2-24-2-244-2-21-2-2-41-2-2-21-2-21-2-4-4-4-411112222-1-122-1-1-1-100040002200220000000-2000-2110000-1-100000000000000000000
χ5744-4-44444-4-4-4-4-444-444404-44-4-44-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-42-4-42-24-44-2-2042-22-4-22-4223−2300-22-220023−230023−232323−23−2300000000000000000000000000000000000000000000000000000
χ5944-4-444-24-42-4-42-24-44-2-2042-22-4-22-42−232300-22-2200−232300−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6044-4-44-2442-42-4-44-2-4-24-20-2-4-222422-40000-22-2200000000000000000000023−23000000000000000023−23000000000000000000000000
χ6144-4-44-2442-42-4-44-2-4-24-20-2-4-222422-40000-22-22000000000000000000000−23230000000000000000−2323000000000000000000000000
χ6244-4-44-2-24222-42-2-2-4-2-210-221-12-2-12223−23001-11-100−330023−23−3−33300000000023−230000003-300000000−33000000000000000000000000
χ6344-4-44-2-24222-42-2-2-4-2-210-221-12-2-12223−23001-11-100−330023−23−3−333000000000−2323000000-33000000003−3000000000000000000000000
χ6444-4-44-2-24222-42-2-2-4-2-210-221-12-2-122−2323001-11-1003−300−232333−3−300000000023−23000000-3300000000−33000000000000000000000000
χ6544-4-44-2-24222-42-2-2-4-2-210-221-12-2-122−2323001-11-1003−300−232333−3−3000000000−23230000003-3000000003−3000000000000000000000000
χ6644-4-4-244-2-4-4-42-4442-2-240-224-42-2-4220000-22-2200000000000000000−2i32i30000000000000000000000−2i32i30000000000000000000000
χ6744-4-4-244-2-4-4-42-4442-2-240-224-42-2-4220000-22-22000000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000000
χ6844-4-4-24-2-2-42-422-242-21-20-2-1-222122-123−23001-11-10023−2300−33−3−33300000−2i32i30000000000000000000000i3−i3003i−3i000000000000000000
χ6944-4-4-24-2-2-42-422-242-21-20-2-1-222122-123−23001-11-10023−2300−33−3−333000002i3−2i30000000000000000000000−i3i300−3i3i000000000000000000
χ7044-4-4-24-2-2-42-422-242-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−300000−2i32i30000000000000000000000i3−i300−3i3i000000000000000000
χ7144-4-4-24-2-2-42-422-242-21-20-2-1-222122-1−2323001-11-100−2323003−333−3−3000002i3−2i30000000000000000000000−i3i3003i−3i000000000000000000
χ724-44-4444-444-44-4-4-4-44440-4-4-44-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-2-44-2-4422-4-44-2-20-422-2-4224-20000-222-2000000000000000000000000000000000000000000000000000023−2300000000000
χ744-44-444-2-44-2-4422-4-44-2-20-422-2-4224-20000-222-20000000000000000000000000000000000000000000000000000−232300000000000
χ754-44-44-24-4-2424-4-42-4-24-202-42-22-42-240000-222-20000000000000000000000000000000000000000000000000000000023−230000000
χ764-44-44-24-4-2424-4-42-4-24-202-42-22-42-240000-222-200000000000000000000000000000000000000000000000000000000−23230000000
χ774-44-4-244244-4-2-4-4-42-2-24022-4422-4-2-20000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ784-44-4-244244-4-2-4-4-42-2-24022-4422-4-2-20000-222-20000000000000000000000000000000000000000000000000000000000−232300000
χ794-4-4444-2-4-424-4-22-444-2-20-4-22242-2-420000-2-22200000000000000000000000004i−4i000000000000000000000000000−2i2i000000000
χ804-4-4444-2-4-424-4-22-444-2-20-4-22242-2-420000-2-2220000000000000000000000000−4i4i0000000000000000000000000002i−2i000000000
χ814-4-444-24-42-4-2-44-424-24-202422-2-4-22-4004i−4i-2-2220000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000000
χ824-4-444-24-42-4-2-44-424-24-202422-2-4-22-400−4i4i-2-22200000000000000000002i−2i00−4i4i0000000000000000002i−2i00000000000000000000
χ834-4-44-2442-4-4424-4-4-2-2-2402-2-4-4-22422004i−4i-2-22200000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000000
χ844-4-44-2442-4-4424-4-4-2-2-2402-2-4-4-2242200−4i4i-2-2220000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000000
χ854-4-44-2-2422-4-224-42-21-2-20-1-22212-2-12004i−4i11-1-100003i−3i003i−3i3i−3i0000000−2i2i00−2i2i0000000000003-30000i−i00000000000000000000
χ864-4-44-2-2422-4-224-42-21-2-20-1-22212-2-12004i−4i11-1-10000−3i3i00−3i3i−3i3i0000000−2i2i00−2i2i000000000000-330000i−i00000000000000000000
χ874-4-44-2-2422-4-224-42-21-2-20-1-22212-2-1200−4i4i11-1-100003i−3i003i−3i3i−3i00000002i−2i002i−2i000000000000-330000−ii00000000000000000000
χ884-4-44-2-2422-4-224-42-21-2-20-1-22212-2-1200−4i4i11-1-10000−3i3i00−3i3i−3i3i00000002i−2i002i−2i0000000000003-30000−ii00000000000000000000
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
χ9188-8-8-4-48-44-844-88-442-4-4024-44-2-44-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-243−4300-11-1100−232300−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-444444-4-4422202-22-2-22-2-2-2−434300-11-110023−230023−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-8-4-448444-8-4-42044-2244-2-4-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-448-4-8-444-84-42-404-24-44-24-4200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-484-4-8-8442-4-40-244-4-2442-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4-44-444442220-2-2-22-2-2-2220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4-44-444442220-2-2-22-2-2-2220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844-4-8-4448-4-4204-4-2-2-44244000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-8484-44-8-4-42-404244-4-2-44-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-444-42220-22-2-22-22-2-20000-1-11100006i−6i00−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-444-42220-22-2-22-22-2-20000-1-1110000−6i6i003i−3i3i−3i00000000000000000000000000000000000000000000000000000

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