Finite Group Databasebeta

← Group #13168751

Character table — Group #13168751

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212224436661212121212121212121212122244666666661212121212121212441212121266666666121212121212121244444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1111111-1-11111111111111-1-1-111111-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-11-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-1-111111111-1-11-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-1111111-1111-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-111111111-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111111111-1-1-1-111-1-1-111111-1-1-11-1-11-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1111-1-11111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111-1-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111-1-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-11-1-1-1-1-111-111111-1-11-1-11111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-111-1-11111111111-1-1111-1-1-1-1-111-11-1-11-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-111-1-11111111-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1111-1-11
χ17222222-12-1222-1-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-122-1-1-1-1-1-1-1-12202222222-1-1-1-1000000000000-1-1-1-1-1-1-1-102-1-100000202000-1-100-1000
χ18222222-12-1222-1-1222-1-122-1-1-12-1-1-12222200-1-1-1-12-122-1-1-1-1-1-1-1-12-20-2-2-22222-1-111000000000000-1111-1-1-1-10-21100000-20-200011001000
χ19222222-12-1222-1-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-220222-2-2-2-211-1-10000000000001-1-1-1111102-1-100000-20-200011001000
χ20222222-12-1222-1-1222-1-122-1-1-12-1-1-1222-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-2-21111000000000000111111110-21100000202000-1-100-1000
χ21222222-12-1222-1-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-21-2-211111111-220-22222-2-2-1-1110000000000001-1-1-1-1-1110-21100000-2020001100-1000
χ22222222-12-1222-1-1222-1-1-22-1-1-12-1-1-12-2-22200-1-1-1-1-21-2-211111111-2-202-2-222-2-2-1-1-1-10000000000001111-1-11102-1-10000020-2000-1-1001000
χ23222222-12-1222-1-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-21-2-211111111220-222-2-2221111000000000000-1-1-1-111-1-10-2110000020-2000-1-1001000
χ24222222-12-1222-1-1222-1-1-22-1-1-12-1-1-12-2-2-2-200-1-1-1-1-21-2-2111111112-202-2-2-2-22211-1-1000000000000-111111-1-102-1-100000-2020001100-1000
χ2522222-1222-1-1222-12-12-12-12-1-1-12-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1202000-1-1-1-12200-1-1-1-12222-1-1-1-12000-1-1-1-12000-1-1-1-120000-1-100000000
χ2622222-1222-1-1222-12-12-12-12-1-1-12-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-120-2000-1-1-1-122001111-2-2-2-211112000-1-1-1-1-20001111-200001100000000
χ2722222-1222-1-1222-12-12-12-12-1-1-12-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-2020001111-2-200-1-1-1-122-2-21111-200011112000-1-1-1-1-200001100000000
χ2822222-1222-1-1222-12-12-12-12-1-1-12-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-20001111-2-2001111-2-222-1-1-1-1-20001111-2000111120000-1-100000000
χ2922222-1222-1-1222-12-12-1-2-12-1-1-12-12-1112222-1-1-1-1-2-211-2-2111111-20-2000-1-1112200-1-1112222-1-1-1-1-2000-1-111-2000-1-111-200001100000000
χ3022222-1222-1-1222-12-12-1-2-12-1-1-12-12-11122-2-2-1-1-1-1-2-211-2-2111111-202000-1-111220011-1-1-2-2-2-21111-2000-1-111200011-1-120000-1-100000000
χ3122222-1222-1-1222-12-12-1-2-12-1-1-12-12-111-2-222-1-1-1-1-2-211-2-211111120-200011-1-1-2-200-1-11122-2-21111200011-1-1-2000-1-11120000-1-100000000
χ3222222-1222-1-1222-12-12-1-2-12-1-1-12-12-111-2-2-2-2-1-1-1-1-2-211-2-211111120200011-1-1-2-20011-1-1-2-222-1-1-1-1200011-1-1200011-1-1-200001100000000
χ332222-122-1222-1222-1-1-122-1-122-1-12-1-1220022-1-1-1-1-12-1-1-1-122-1-1-1-10222-1-1000000222222-1-100000002-1-10000-1-1-1-1-1-1-1-1002020000-1-10-100
χ342222-122-1222-1222-1-1-122-1-122-1-12-1-1220022-1-1-1-1-12-1-1-1-122-1-1-1-10-22-211000000-2-22222-1-10000000-2110000-1111-1-1-1-100-20-20000110100
χ352222-122-1222-1222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-102-22-1-100000022-2-2-2-21100000002-1-100001-1-1-1111100-20-20000110100
χ362222-122-1222-1222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-211000000-2-2-2-2-2-2110000000-211000011111111002020000-1-10-100
χ372222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-21111-2-2111102-2-2-1-1000000-2-222-2-2-1-100000002-1-100001111-1-1110020-20000-1-10100
χ382222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-21111-2-211110-2-22110000002222-2-2-1-10000000-21100001-1-1-1-1-11100-2020000110-100
χ392222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-21111-2-21111022-2-1-1000000-2-2-2-2221100000002-1-10000-111111-1-100-2020000110-100
χ402222-122-1222-1222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-21111-2-211110-2221100000022-2-222110000000-2110000-1-1-1-111-1-10020-20000-1-10100
χ412-2-22222-2-22-222-2-2-22220-2-2-2-2222-2-2002-22i−2i2-2-220000000000000000002-2002-2002i−2i002i−2i2i−2i2i2i−2i−2i00002-20000002i−2i00000000000000000
χ422-2-22222-2-22-222-2-2-22220-2-2-2-2222-2-2002-2−2i2i2-2-220000000000000000002-2002-200−2i2i00−2i2i−2i2i−2i−2i2i2i00002-2000000−2i2i00000000000000000
χ432-2-22222-2-22-222-2-2-22220-2-2-2-2222-2-200-222i−2i2-2-22000000000000000000-2200-22002i−2i002i−2i−2i2i−2i−2i2i2i0000-220000002i−2i00000000000000000
χ442-2-22222-2-22-222-2-2-22220-2-2-2-2222-2-200-22−2i2i2-2-22000000000000000000-2200-2200−2i2i00−2i2i2i−2i2i2i−2i−2i0000-22000000−2i2i00000000000000000
χ452-2-222-12-2-2-1122-21-2-12-101-211-12-1-21−i3i32-22i−2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-200−ii3−32i−2i2i−2i−i−iii0000-11−i3i30000−ii3−3000003−300000000
χ462-2-222-12-2-2-1122-21-2-12-101-211-12-1-21−i3i32-2−2i2i-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32-200i−i−33−2i2i−2i2iii−i−i0000-11−i3i30000i−i−3300000−3300000000
χ472-2-222-12-2-2-1122-21-2-12-101-211-12-1-21−i3i3-222i−2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-2200−ii3−32i−2i−2i2iii−i−i00001-1i3−i30000−ii3−300000−3300000000
χ482-2-222-12-2-2-1122-21-2-12-101-211-12-1-21−i3i3-22−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3-2200i−i−33−2i2i2i−2i−i−iii00001-1i3−i30000i−i−33000003−300000000
χ492-2-222-12-2-2-1122-21-2-12-101-211-12-1-21i3−i32-22i−2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-200−ii−332i−2i2i−2i−i−iii0000-11i3−i30000−ii−3300000−3300000000
χ502-2-222-12-2-2-1122-21-2-12-101-211-12-1-21i3−i32-2−2i2i-111-100i3−i300i3−i3i3i3−i3−i3000000-11i3−i32-200i−i3−3−2i2i−2i2iii−i−i0000-11i3−i30000i−i3−3000003−300000000
χ512-2-222-12-2-2-1122-21-2-12-101-211-12-1-21i3−i3-222i−2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-2200−ii−332i−2i−2i2iii−i−i00001-1−i3i30000−ii−33000003−300000000
χ522-2-222-12-2-2-1122-21-2-12-101-211-12-1-21i3−i3-22−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000001-1−i3i3-2200i−i3−3−2i2i2i−2i−i−iii00001-1−i3i30000i−i3−300000−3300000000
χ5344444-2-24-2-2-24-2-2-24-2-214-2-211-2-21-2-2-2-2440011114-2-2-2-2-2111111400000-2-2-2-2-2-200000000000000-2000111100000000000000000000000
χ5444444-2-24-2-2-24-2-2-24-2-214-2-211-2-21-2-2-2-2-4-40011114-2-2-2-2-2111111-400000222222000000000000002000-1-1-1-100000000000000000000000
χ5544444-2-24-2-2-24-2-2-24-2-21-4-2-211-2-21-2-22244001111-422222-1-1-1-1-1-1-400000-2-222-2-200000000000000200011-1-100000000000000000000000
χ5644444-2-24-2-2-24-2-2-24-2-21-4-2-211-2-21-2-222-4-4001111-422222-1-1-1-1-1-140000022-2-22200000000000000-2000-1-11100000000000000000000000
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χ594444-24-2-2-244-2-2-24-2-21-2-4-21-2-2-21-21-2-4-4000011112222-1-122-1-1-1-1040-4-2-2000000220000000000000-211000002-1-10000000000000000000
χ604444-24-2-2-244-2-2-24-2-21-2-4-21-2-2-21-21-2-4-4000011112222-1-122-1-1-1-10-40422000000-2-200000000000002-1-100000-2110000000000000000000
χ614444-2-24-24-2-2-244-2-21-2-241-2-2-21-2-2-21-2-200441111-2411-2-2-2-2111100400000000000-2-2-2-2-2-200000000000000-20001111000000000000000
χ624444-2-24-24-2-2-244-2-21-2-241-2-2-21-2-2-21-2-200-4-41111-2411-2-2-2-2111100-400000000000222222000000000000002000-1-1-1-1000000000000000
χ634444-2-24-24-2-2-244-2-21-2-2-41-2-2-21-2-2-2122004411112-4-1-12222-1-1-1-100-400000000000-2-222-2-200000000000000200011-1-1000000000000000
χ644444-2-24-24-2-2-244-2-21-2-2-41-2-2-21-2-2-212200-4-411112-4-1-12222-1-1-1-10040000000000022-2-22200000000000000-2000-1-111000000000000000
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χ864-4-444-2-2-42-224-222-4-2-21022-1-1-2-2122−2i32i3-44001-1-1100−2i32i300i3−i3i3i3−i3−i30000002-22i3−2i32-2000000000000000000-11−i3i300000000000000000000000
χ874-4-444-2-2-42-224-222-4-2-21022-1-1-2-21222i3−2i34-4001-1-11002i3−2i300−i3i3−i3−i3i3i3000000-222i3−2i3-220000000000000000001-1−i3i300000000000000000000000
χ884-4-444-2-2-42-224-222-4-2-21022-1-1-2-21222i3−2i3-44001-1-11002i3−2i300−i3i3−i3−i3i3i30000002-2−2i32i32-2000000000000000000-11i3−i300000000000000000000000
χ894-4-44-2442-44-4-24-4-42-2-24022-4-4-2-242200004i−4i-222-2000000000000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000
χ904-4-44-2442-44-4-24-4-42-2-24022-4-4-2-24220000−4i4i-222-200000000000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000
χ914-4-44-2-242-4-22-24-4221-2-20-12221-2-22-1−2i32i3004i−4i1-1-1100i3−i300−2i32i3i3i3−i3−i300000000000000−2i2i23−23−2i2i000000000000000000i−i−33000000000000000
χ924-4-44-2-242-4-22-24-4221-2-20-12221-2-22-1−2i32i300−4i4i1-1-1100i3−i300−2i32i3i3i3−i3−i3000000000000002i−2i−23232i−2i000000000000000000−ii3−3000000000000000
χ934-4-44-2-242-4-22-24-4221-2-20-12221-2-22-12i3−2i3004i−4i1-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000000−2i2i−2323−2i2i000000000000000000i−i3−3000000000000000
χ944-4-44-2-242-4-22-24-4221-2-20-12221-2-22-12i3−2i300−4i4i1-1-1100−i3i3002i3−2i3−i3−i3i3i3000000000000002i−2i23−232i−2i000000000000000000−ii−33000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-48-44-4-8444-8-4-420-4-42-244-24400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-48-484-44-8-8442-4-402-4-44-2444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-2000000-1-11100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-2000000-1-1110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-4-8444-84-4-48-4-42044-2244-2-4-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-444-8-844-48-4-42-404-24-44-242-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-484-8444-88-4-42-4-40-244-4-244-420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444444-4-4-42220-2-2-22-2-2-222000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444444-4-4-42220-2-2-22-2-2-222000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4448-8-4-44-84-42-404-244-42-4-240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-44-4-44442220-2-2-2-2222-2-2−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-44-4-44442220-2-2-2-2222-2-24i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000

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