Finite Group Databasebeta

← Group #13168074

Character table — Group #13168074

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666223666121212121212121212121212122444466666612121212121244666661212121212121212121212121222444661212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-11111111-11-11111-1-1-1-111-1-1-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-11111111-1-111-1-111-1-1-111-1-11-111111-1-11111-1-1-111-1-1-1-111-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-11-111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-111
χ511111111111111111111111111111-1-11111111111111111111-111-1-1-1-111111111111-1-111-111-11-1-1111111-1-11-1-1-1-111-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-111-1-1-1-11-1-111-11-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-1-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-1-1-111111-1-1-1-11-1-1-1-111-1-11-11-1111-1-1-1-1-1-1-1111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-11-111111111-1-1-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-11111-1-111-111-1-1-11-1-11-1-11111-1-1-11-1-11-1-111-1-11111-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-111-1-1-111-1-1-1-111-1-111-1111-1-1-1-1-111-1-11-111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1-1111-1-1-1-1-111111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-1-1-111111-1-1111-111-111-1-1-1-111-11-1-11-1-111-1-1-1-111-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-111111111-1-11-1-11-1111111-1-1-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-11111-1-1111-11-1111-1-1-1-111-111-1
χ17222222-12-1-1-1222222-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-12220022-1-1-1-1002200002-1-1-1-1-1-1020-1-1-1-1000022000-1-1000000-1000
χ18222222-12-1-1-1222222-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-220022-1-11100-2-20000-2-1-111-11020-1-1110000-2-2000110000001000
χ19222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-122-200-2-211-1-100220000211-1-11-10-2011-1-10000-2-2000110000001000
χ20222222-12-1-1-1222222-1-122-1-12-1-1-1-12-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-200-2-2111100-2-20000-21111110-201111000022000-1-1000000-1000
χ21222222-12-1-1-1222222-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-2-2-2111111112-2-20022-1-1-1-100-2-200002-1-1-1-1110-20111100002-2000-1-10000001000
χ22222222-12-1-1-1222222-1-1-22-1-12-1-1-1-1222-1-1-1-11-2-2-2-211111111-22-20022-1-11100220000-2-1-1111-10-2011-1-10000-2200011000000-1000
χ23222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-2-2-2111111112-2200-2-211-1-100-2-20000211-1-1-11020-1-1110000-2200011000000-1000
χ24222222-12-1-1-1222222-1-1-22-1-12-1-1-1-12-2-2-1-1-1-11-2-2-2-211111111-22200-2-2111100220000-21111-1-1020-1-1-1-100002-2000-1-10000001000
χ2522222-122222-12-1-12-12-12-12-1-12-12-1-100-1-1-1-122-1-1-122-1-1-1-1-1-122022000022-1-1-1-12222-100-1-102-10200-1-1-1-1-1-10020000-1-1000000-10
χ2622222-122222-12-1-12-12-12-12-1-12-12-1-100-1-1-1-122-1-1-122-1-1-1-1-1-1220-2-200002211-1-1-2-2-2-2-100-1-10210-200-1-1111100-200001100000010
χ2722222-122222-12-1-12-12-12-12-1-12-12-1-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-20220000-2-2-1-11122-2-2100110-2-1020011-1-1-1-100-200001100000010
χ2822222-122222-12-1-12-12-12-12-1-12-12-1-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-20-2-20000-2-21111-2-222100110-210-2001111110020000-1-1000000-10
χ2922222-122222-12-1-12-12-1-2-12-1-12-12-1-100-1-1-1-1-2-2111-2-21111112-202-2000022-1-111-2-2-2-2-100-1-10-21020011-1-111002000011000000-10
χ3022222-122222-12-1-12-12-1-2-12-1-12-12-1-100-1-1-1-1-2-2111-2-21111112-20-2200002211112222-100-1-10-2-10-2001111-1-100-20000-1-100000010
χ3122222-122222-12-1-12-12-1-2-12-1-12-12-1-100-1-1-1-1-2-2111-2-2111111-2202-20000-2-2-1-1-1-1-2-222100110210200-1-1-1-11100-20000-1-100000010
χ3222222-122222-12-1-12-12-1-2-12-1-12-12-1-100-1-1-1-1-2-2111-2-2111111-220-220000-2-211-1-122-2-21001102-10-200-1-111-1-1002000011000000-10
χ332222-122-12222-122-1-1-122-1-12-1-12-12-122-1-1-1-12-12-1-1-1-122-1-1-1-100222-1-122002200-1-1000-1-100202-1-1-1-100-1-1-1-1000220000-1-1000-100
χ342222-122-12222-122-1-1-122-1-12-1-12-12-122-1-1-1-12-12-1-1-1-122-1-1-1-1002-2-2-1-12200-2-20011000-1-10020-2-11-1-1001111000-2-2000011000100
χ352222-122-12222-122-1-1-122-1-12-1-12-12-1-2-2-1-1-1-12-12-1-1-1-122-1-1-1-100-22211-2-2002200-1-10001100-2021-11100-1-1-1-1000-2-2000011000100
χ362222-122-12222-122-1-1-122-1-12-1-12-12-1-2-2-1-1-1-12-12-1-1-1-122-1-1-1-100-2-2-211-2-200-2-200110001100-20-21111001111000220000-1-1000-100
χ372222-122-12222-122-1-1-12-2-1-12-1-12-12-122-1-1-1-1-21-21111-2-2111100-22-2-1-12200220011000-1-100-20-21-11100-1-111000-22000011000-100
χ382222-122-12222-122-1-1-12-2-1-12-1-12-12-122-1-1-1-1-21-21111-2-2111100-2-22-1-12200-2-200-1-1000-1-100-20211110011-1-10002-20000-1-1000100
χ392222-122-12222-122-1-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-21-21111-2-211110022-211-2-200220011000110020-2-1-1-1-100-1-1110002-20000-1-1000100
χ402222-122-12222-122-1-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-21-21111-2-21111002-2211-2-200-2-200-1-10001100202-11-1-10011-1-1000-22000011000-100
χ4122-2-22222-22-2-2-2-22-2222022-2-2-2-2-22-22-222-2-20000000000000000002-22-2000000002i−2i02-200000000000000000000002i−2i002i−2i0000
χ4222-2-22222-22-2-2-2-22-2222022-2-2-2-2-22-22-222-2-20000000000000000002-22-200000000−2i2i02-20000000000000000000000−2i2i00−2i2i0000
χ4322-2-22222-22-2-2-2-22-2222022-2-2-2-2-22-2-2222-2-2000000000000000000-22-22000000002i−2i0-2200000000000000000000002i−2i00−2i2i0000
χ4422-2-22222-22-2-2-2-22-2222022-2-2-2-2-22-2-2222-2-2000000000000000000-22-2200000000−2i2i0-220000000000000000000000−2i2i002i−2i0000
χ4544444-2-24-2-2-2-24-2-24-2-214-2-21-2-21-21-2001111-24-2-2-2-2-2111111440000000-2-200-2-20000-200110-20000011000000000000000000000
χ4644444-2-24-2-2-2-24-2-24-2-214-2-21-2-21-21-2001111-24-2-2-2-2-2111111-4-400000002200220000200-1-10200000-1-1000000000000000000000
χ4744444-2-24-2-2-2-24-2-24-2-21-4-2-21-2-21-21-20011112-422222-1-1-1-1-1-14-40000000-2-200220000-200110200000-1-1000000000000000000000
χ4844444-2-24-2-2-2-24-2-24-2-21-4-2-21-2-21-21-20011112-422222-1-1-1-1-1-1-4400000002200-2-20000200-1-10-20000011000000000000000000000
χ494444-24-2-2-2-2-24-244-2-21-24-21-2-21-21-2-2441111-2-24-2-211-2-2111100400-2-2-2-2000000000001100-200-201100000000000000000000000
χ504444-24-2-2-2-2-24-244-2-21-24-21-2-21-21-2-2-4-41111-2-24-2-211-2-2111100-400222200000000000-1-10020020-1-100000000000000000000000
χ514444-24-2-2-2-2-24-244-2-21-2-4-21-2-21-21-2-244111122-422-1-122-1-1-1-100-400-2-2-2-200000000000110020020-1-100000000000000000000000
χ524444-24-2-2-2-2-24-244-2-21-2-4-21-2-21-21-2-2-4-4111122-422-1-122-1-1-1-100400222200000000000-1-100-200-201100000000000000000000000
χ534444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-210011114-2-211-2-2-2-2111100044000000-2-200-2-2000000000-20-20000111100000000000000000
χ544444-2-24-2444-2-2-2-2-21-2-241-2-21-2-2-2-210011114-2-211-2-2-2-21111000-4-40000002200220000000002020000-1-1-1-100000000000000000
χ554444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-21001111-422-1-12222-1-1-1-10004-4000000-2-2002200000000020-2000011-1-100000000000000000
χ564444-2-24-2444-2-2-2-2-21-2-2-41-2-21-2-2-2-21001111-422-1-12222-1-1-1-1000-440000002200-2-2000000000-2020000-1-11100000000000000000
χ5744-4-444-242-22-4-4-44-44-2-204-22-4222-2-44-4-2-2220000000000000000004-4-2200000000000-2200000000000000000000000000000000
χ5844-4-444-242-22-4-4-44-44-2-204-22-4222-2-4-44-2-222000000000000000000-442-2000000000002-200000000000000000000000000000000
χ5944-4-44-244-44-42-42-2-4-24-20-2422-42-4-2200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ6044-4-44-244-44-42-42-2-4-24-20-2422-42-4-2200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ6144-4-4-244-2-44-4-42-442-2-240-2-2-422-42424-4-2-222000000000000000000-224-400000000000-2200000000000000000000000000000000
χ6244-4-4-244-2-44-4-42-442-2-240-2-2-422-4242-44-2-2220000000000000000002-2-44000000000002-200000000000000000000000000000000
χ6344-4-4-24-2-22-22-42-442-21-20-2122-12-1-224-411-1-1000003i−3i003i3i−3i−3i00000-22-22000000000001-100000003i−3i00000000000000000000000
χ6444-4-4-24-2-22-22-42-442-21-20-2122-12-1-224-411-1-100000−3i3i00−3i−3i3i3i00000-22-22000000000001-10000000−3i3i00000000000000000000000
χ6544-4-4-24-2-22-22-42-442-21-20-2122-12-1-22-4411-1-1000003i−3i003i3i−3i−3i000002-22-200000000000-110000000−3i3i00000000000000000000000
χ6644-4-4-24-2-22-22-42-442-21-20-2122-12-1-22-4411-1-100000−3i3i00−3i−3i3i3i000002-22-200000000000-1100000003i−3i00000000000000000000000
χ674-44-4444-4-4-444-4-4-444440-4-44-4-4-44-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-422-24-4-4-444-2-20-42-2-422-22400-22-220000000000000000000000−2i32i300000000000−2i32i3000000000000000000000000000000
χ694-44-444-2-422-24-4-4-444-2-20-42-2-422-22400-22-2200000000000000000000002i3−2i3000000000002i3−2i3000000000000000000000000000000
χ704-44-44-24-4-4-44-2-4224-24-202-4-22-4242-200-22-220000000000000000000000000023−23000000000000000023−23000000000000000000000
χ714-44-44-24-4-4-44-2-4224-24-202-4-22-4242-200-22-2200000000000000000000000000−23230000000000000000−2323000000000000000000000
χ724-44-44-2-2-422-2-2-4224-2-21022122-1-2-1-2001-11-100000003i−3i3i−3i3i−3i000000000−2i32i30023−230000000i3−i30000000−33000000000000000000000
χ734-44-44-2-2-422-2-2-4224-2-21022122-1-2-1-2001-11-100000003i−3i3i−3i3i−3i0000000002i3−2i300−23230000000−i3i300000003−3000000000000000000000
χ744-44-44-2-2-422-2-2-4224-2-21022122-1-2-1-2001-11-10000000−3i3i−3i3i−3i3i000000000−2i32i300−23230000000i3−i300000003−3000000000000000000000
χ754-44-44-2-2-422-2-2-4224-2-21022122-1-2-1-2001-11-10000000−3i3i−3i3i−3i3i0000000002i3−2i30023−230000000−i3i30000000−33000000000000000000000
χ764-44-4-2442-4-4442-4-4-2-2-24022422-4-2-4-200-22-2200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ774-44-4-2442-4-4442-4-4-2-2-24022422-4-2-4-200-22-22000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ784-4-44444-44-4-4-444-4-44440-4-4-4444-4-4-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-222-444-4-44-2-20-4224-2-222-400-222-20000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ804-4-4444-2-4-222-444-4-44-2-20-4224-2-222-400-222-200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ814-4-444-24-44-4-424-22-4-24-202-42-24-2-42200-222-200000000000000000000000023−230000000000000000000023−230000000000000000000
χ824-4-444-24-44-4-424-22-4-24-202-42-24-2-42200-222-2000000000000000000000000−232300000000000000000000−23230000000000000000000
χ834-4-44-24424-4-4-4-24-42-2-24022-4-2-242-4200-222-2000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ844-4-44-24424-4-4-4-24-42-2-24022-4-2-242-4200-222-20000000000000000000000000000−2323000000000000000000−232300000000000000000
χ854-4-44-2-2424-4-42-2-2221-2-20-1221-2-222-1001-1-110003-300003-3-330000000000023−230023−230000000000000000−33−3300000000000000000
χ864-4-44-2-2424-4-42-2-2221-2-20-1221-2-222-1001-1-110003-300003-3-3300000000000−232300−232300000000000000003−33−300000000000000000
χ874-4-44-2-2424-4-42-2-2221-2-20-1221-2-222-1001-1-11000-330000-333-30000000000023−2300−23230000000000000000−333−300000000000000000
χ884-4-44-2-2424-4-42-2-2221-2-20-1221-2-222-1001-1-11000-330000-333-300000000000−23230023−2300000000000000003−3−3300000000000000000
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
χ9188-8-88-4-484-444-84-4-8-4-420-4-4-244-24240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4-88-8444-442-4-402-44-2444-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44444-44222022-2-2-2-2-22-200-1-111000006i−6i00−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-44444-44222022-2-2-2-2-22-200-1-11100000−6i6i003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4444-484-8-8-4-42-404-2-44-2424-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-8-88-4444-42-4-40-24-4-244-442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-4-4444-42220-2-22-2-2-22-2200-11-1100000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444-4-4444-42220-2-22-2-2-22-2200-11-110000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-8-44448-44-8-4-42044-2-4-424-24002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-444-8-48-84-42-404-24-42-4-244002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4444-4-4442220-2-2-2222-2-2-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4444-4-4442220-2-2-2222-2-2-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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