Finite Group Databasebeta

← Group #13168228

Character table — Group #13168228

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666622366612121212121212121212121212244446666661212121212124466666121212121212121212121212122444412121212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-11111111-11-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11-1
χ3111111111111111111111111111111111111111111111111-1-11111111-1-11111-1-1-1-1-111-1-11-111111-1-11111-11-1-11-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-11-111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-11
χ511111111111111111111111111111-1-11111111111111111111-111-1-1-1-111111111111-1-111-111-11-1-11111111-1-1-1-111-1-1-1-1-1-11-1-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-111-1-11-1-111-11-1-1-1-1-111-1-1-1-1-11-1-11-1-111-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1-11111-1-111
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-111-1-111-1-1-1-111-111-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1111-11-11-1-111-1-1-1-11-111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-1-1-111-1-1-11-1-11-1-11111-1-111-11-1-1-1-1-111-1-111-11
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-111-1-1-111-1-1-1-111-1-111-1-1-11111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1111-1-1111-1-11111-1-111-1-1-1-1-111111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-111-1-1-1-11-1-1111-111-111-1-1-1-11111-11-1-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-111-111111111-1-11-11-11-1-111-1-1111-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-11111-1-111-111-1-111-1-1-1-1-1-1-1111
χ17222222-122-12-12-122-12-12-12-1-12-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1220220000-1-1-1-1222222200-1-10-1-10200-1-1-1-1-1-120000-1-1000000-1000
χ18222222-122-12-12-122-12-12-12-1-12-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1220-2-20000-1-111-2-222-2-2200-1-10-110-200-1-11111-20000110000001000
χ19222222-122-12-12-122-12-12-12-1-12-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-2022000011-1-122-2-2-2-2-2001101-1020011-1-1-1-1-20000110000001000
χ20222222-122-12-12-122-12-12-12-1-12-12-1-100-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-20-2-200001111-2-2-2-222-200110110-20011111120000-1-1000000-1000
χ21222222-122-12-12-122-12-1-2-12-1-12-12-1-100-1-1-1-1-21-2-2-2111111112-202-20000-1-1-1-1-2-2-2-222200-1-1011020011-1-111-20000-1-10000001000
χ22222222-122-12-12-122-12-1-2-12-1-12-12-1-100-1-1-1-1-21-2-2-2111111112-20-220000-1-11122-2-2-2-2200-1-101-10-2001111-1-12000011000000-1000
χ23222222-122-12-12-122-12-1-2-12-1-12-12-1-100-1-1-1-1-21-2-2-211111111-2202-2000011-1-1-2-222-2-2-200110-110200-1-1-1-1112000011000000-1000
χ24222222-122-12-12-122-12-1-2-12-1-12-12-1-100-1-1-1-1-21-2-2-211111111-220-2200001111222222-200110-1-10-200-1-111-1-1-20000-1-10000001000
χ2522222-122-12-12222-12-1-122-1-12-1-1-1-1222-1-1-1-1-122-1-122-1-1-1-1-1-12220022-1-1220000-1-100-1-1-1-1-1-12020-1-1-1-10000002200000-1-10000-10
χ2622222-122-12-12222-12-1-122-1-12-1-1-1-1222-1-1-1-1-122-1-122-1-1-1-1-1-1-2-220022-1-1-2-2000011001-1-111-1-2020-1-111000000-2-20000011000010
χ2722222-122-12-12222-12-1-122-1-12-1-1-1-12-2-2-1-1-1-1-122-1-122-1-1-1-1-1-122-200-2-211220000-1-100-111-1-1120-2011-1-1000000-2-20000011000010
χ2822222-122-12-12222-12-1-122-1-12-1-1-1-12-2-2-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-200-2-211-2-200001100111111-20-2011110000002200000-1-10000-10
χ2922222-122-12-12222-12-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-211-2-21111112-2-20022-1-12200001100-1-1-1-1-11-20-2011110000002-200000110000-10
χ3022222-122-12-12222-12-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-211-2-2111111-22-20022-1-1-2-20000-1-1001-1-111120-2011-1-1000000-2200000-1-1000010
χ3122222-122-12-12222-12-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-211-2-21111112-2200-2-2112200001100-111-1-1-1-2020-1-111000000-2200000-1-1000010
χ3222222-122-12-12222-12-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-211-2-2111111-22200-2-211-2-20000-1-10011111-12020-1-1-1-10000002-200000110000-10
χ332222-122-12222-12-12-1-122-1-12-1-12-12-122-1-1-1-122-1-1-1-1-122-1-1-1-100222-1-1220022-1-100000-1-100202-1-1-1-100-1-1-1-10200200-1-100000-100
χ342222-122-12222-12-12-1-122-1-12-1-12-12-122-1-1-1-122-1-1-1-1-122-1-1-1-1002-2-2-1-12200-2-21100000-1-10020-2-11-1-10011110-200-2001100000100
χ352222-122-12222-12-12-1-122-1-12-1-12-12-1-2-2-1-1-1-122-1-1-1-1-122-1-1-1-100-22211-2-20022-1-1000001100-2021-11100-1-1-1-10-200-2001100000100
χ362222-122-12222-12-12-1-122-1-12-1-12-12-1-2-2-1-1-1-122-1-1-1-1-122-1-1-1-100-2-2-211-2-200-2-211000001100-20-211110011110200200-1-100000-100
χ372222-122-12222-12-12-1-12-2-1-12-1-12-12-122-1-1-1-1-2-211111-2-2111100-22-2-1-12200221100000-1-100-20-21-11100-1-1110200-2001100000-100
χ382222-122-12222-12-12-1-12-2-1-12-1-12-12-122-1-1-1-1-2-211111-2-2111100-2-22-1-12200-2-2-1-100000-1-100-20211110011-1-10-200200-1-100000100
χ392222-122-12222-12-12-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-2-211111-2-211110022-211-2-200221100000110020-2-1-1-1-100-1-1110-200200-1-100000100
χ402222-122-12222-12-12-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-2-211111-2-21111002-2211-2-200-2-2-1-1000001100202-11-1-10011-1-10200-2001100000-100
χ412-22-22222-2-2-22-2-2-22222022-2-2-2-2-22-22-222-2-20000000000000000002-22-2000000002i−2i02-2000000000000000000002i−2i00002i−2i0000
χ422-22-22222-2-2-22-2-2-22222022-2-2-2-2-22-22-222-2-20000000000000000002-22-200000000−2i2i02-200000000000000000000−2i2i0000−2i2i0000
χ432-22-22222-2-2-22-2-2-22222022-2-2-2-2-22-2-2222-2-2000000000000000000-22-22000000002i−2i0-22000000000000000000002i−2i0000−2i2i0000
χ442-22-22222-2-2-22-2-2-22222022-2-2-2-2-22-2-2222-2-2000000000000000000-22-2200000000−2i2i0-2200000000000000000000−2i2i00002i−2i0000
χ4544444-2-24-2-2-2-24-24-2-2-214-2-21-2-21-21-2001111-2-24-2-2-2-2111111440000000-2-20000-2-200-200110-20000011000000000000000000000
χ4644444-2-24-2-2-2-24-24-2-2-214-2-21-2-21-21-2001111-2-24-2-2-2-2111111-4-400000002200002200200-1-10200000-1-1000000000000000000000
χ4744444-2-24-2-2-2-24-24-2-2-21-4-2-21-2-21-21-200111122-42222-1-1-1-1-1-14-40000000-2-200002200-200110200000-1-1000000000000000000000
χ4844444-2-24-2-2-2-24-24-2-2-21-4-2-21-2-21-21-200111122-42222-1-1-1-1-1-1-440000000220000-2-200200-1-10-20000011000000000000000000000
χ494444-24-2-24-24-2-2-2-241-2-241-2-21-2-2-2-210011114-2-2-2-211-2-2111100044000000-2-2-2-200000000000-20-20000111100000000000000000
χ504444-24-2-24-24-2-2-2-241-2-241-2-21-2-2-2-210011114-2-2-2-211-2-21111000-4-40000002222000000000002020000-1-1-1-100000000000000000
χ514444-24-2-24-24-2-2-2-241-2-2-41-2-21-2-2-2-21001111-42222-1-122-1-1-1-10004-4000000-2-2220000000000020-2000011-1-100000000000000000
χ524444-24-2-24-24-2-2-2-241-2-2-41-2-21-2-2-2-21001111-42222-1-122-1-1-1-1000-4400000022-2-200000000000-2020000-1-11100000000000000000
χ534444-2-24-2-24-24-24-2-2-21-24-21-2-21-21-2-2441111-24-211-2-2-2-2111100400-2-2-2-2000000000001100-200-201100000000000000000000000
χ544444-2-24-2-24-24-24-2-2-21-24-21-2-21-21-2-2-4-41111-24-211-2-2-2-2111100-400222200000000000-1-10020020-1-100000000000000000000000
χ554444-2-24-2-24-24-24-2-2-21-2-4-21-2-21-21-2-24411112-42-1-12222-1-1-1-100-400-2-2-2-200000000000110020020-1-100000000000000000000000
χ564444-2-24-2-24-24-24-2-2-21-2-4-21-2-21-21-2-2-4-411112-42-1-12222-1-1-1-100400222200000000000-1-100-200-201100000000000000000000000
χ5744-4-4444-444-4-44-4-4-44440-4-4-4444-4-4-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-2-4242-4-4-24-202-42-24-2-42200-222-200000000000000000000000023−230000000000000000000023−230000000000000000000
χ5944-4-444-2-44-2-4242-4-4-24-202-42-24-2-42200-222-2000000000000000000000000−232300000000000000000000−23230000000000000000000
χ6044-4-44-24-4-242-44-4-424-2-20-4224-2-222-400-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ6144-4-44-24-4-242-44-4-424-2-20-4224-2-222-400-222-200000000000000000000000000000000000000000000000000000000000−2323000000
χ6244-4-4-244244-4-4-2-42-4-2-24022-4-2-242-4200-222-20000000000000000000000000023−230000000000000000000023−2300000000000000000
χ6344-4-4-244244-4-4-2-42-4-2-24022-4-2-242-4200-222-200000000000000000000000000−232300000000000000000000−232300000000000000000
χ6444-4-4-24-224-2-42-222-41-2-20-1221-2-222-1001-1-11000003-30033-3-30000000000023−2323−23000000000000000000−33−3300000000000000000
χ6544-4-4-24-224-2-42-222-41-2-20-1221-2-222-1001-1-11000003-30033-3-300000000000−2323−23230000000000000000003−33−300000000000000000
χ6644-4-4-24-224-2-42-222-41-2-20-1221-2-222-1001-1-1100000-3300-3-3330000000000023−23−2323000000000000000000−333−300000000000000000
χ6744-4-4-24-224-2-42-222-41-2-20-1221-2-222-1001-1-1100000-3300-3-33300000000000−232323−230000000000000000003−3−3300000000000000000
χ684-44-444-24-42-4-2-42-44-24-20-2422-42-4-2200-2-2220000000000000000000000000000004i−4i00000000000000000000000−2i2i0000000000
χ694-44-444-24-42-4-2-42-44-24-20-2422-42-4-2200-2-222000000000000000000000000000000−4i4i000000000000000000000002i−2i0000000000
χ704-44-44-2442-424-4-4-4-24-2-204-22-4222-2-44-4-2-2220000000000000000004-4-2200000000000-2200000000000000000000000000000000
χ714-44-44-2442-424-4-4-4-24-2-204-22-4222-2-4-44-2-222000000000000000000-442-2000000000002-200000000000000000000000000000000
χ724-44-4-244-2-4-4-442-424-2-240-2-2-422-42424-4-2-222000000000000000000-224-400000000000-2200000000000000000000000000000000
χ734-44-4-244-2-4-4-442-424-2-240-2-2-422-4242-44-2-2220000000000000000002-2-44000000000002-200000000000000000000000000000000
χ744-44-4-2-24-22-4242-42-2-21-20-2122-12-1-224-411-1-10003i−3i00003i−3i3i−3i00000-22-22000000000001-100000003i−3i00000000000000000000000
χ754-44-4-2-24-22-4242-42-2-21-20-2122-12-1-224-411-1-1000−3i3i0000−3i3i−3i3i00000-22-22000000000001-10000000−3i3i00000000000000000000000
χ764-44-4-2-24-22-4242-42-2-21-20-2122-12-1-22-4411-1-10003i−3i00003i−3i3i−3i000002-22-200000000000-110000000−3i3i00000000000000000000000
χ774-44-4-2-24-22-4242-42-2-21-20-2122-12-1-22-4411-1-1000−3i3i0000−3i3i−3i3i000002-22-200000000000-1100000003i−3i00000000000000000000000
χ784-4-44444-4-4-44-4-444-44440-4-44-4-4-44-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-4242-4-24-4-24-202-4-22-4242-200-22-220000000000000000000000−2i32i300000000000−2i32i3000000000000000000000000000000
χ804-4-4444-2-4-4242-4-24-4-24-202-4-22-4242-200-22-2200000000000000000000002i3−2i3000000000002i3−2i3000000000000000000000000000000
χ814-4-444-24-42-4-2-4-44424-2-20-42-2-422-22400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ824-4-444-24-42-4-2-4-44424-2-20-42-2-422-22400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ834-4-444-2-2-422-22-4-242-2-21022122-1-2-1-2001-11-100000003i−3i3i−3i−3i3i000000000−2i32i3000023−2300000i3−i30000000−33000000000000000000000
χ844-4-444-2-2-422-22-4-242-2-21022122-1-2-1-2001-11-100000003i−3i3i−3i−3i3i0000000002i3−2i30000−232300000−i3i300000003−3000000000000000000000
χ854-4-444-2-2-422-22-4-242-2-21022122-1-2-1-2001-11-10000000−3i3i−3i3i3i−3i000000000−2i32i30000−232300000i3−i300000003−3000000000000000000000
χ864-4-444-2-2-422-22-4-242-2-21022122-1-2-1-2001-11-10000000−3i3i−3i3i3i−3i0000000002i3−2i3000023−2300000−i3i30000000−33000000000000000000000
χ874-4-44-2442-4-44-424-2-4-2-24022422-4-2-4-200-22-22000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ884-4-44-2442-4-44-424-2-4-2-24022422-4-2-4-200-22-220000000000000000000000000000000000000000000000000000000002i3−2i300000000
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
χ9188-8-88-4-4-8-4-44484-84-4-42044-2-4-424-24002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-484-8-4-844-42-404-24-42-4-244002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-444-44442220-2-2-2222-2-2-200-111-1000006-600-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-444-44442220-2-2-2222-2-2-200-111-100000-660033-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-48444-4-84-8-4-4-420-4-4-244-24240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-4-84-8-444482-4-402-44-2444-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4444-4444-4222022-2-2-2-2-22-200-1-1110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444-4444-4222022-2-2-2-2-22-200-1-111000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-84844-4-4-82-4-40-24-4-244-442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-8-4-848-44-42-404-2-44-2424-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-444-4-442220-2-22-2-2-22-2200-11-1100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-444-4-442220-2-22-2-2-22-2200-11-110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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