Finite Group Databasebeta

← Group #13178756

Character table — Group #13178756

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size112222222444444444444444488888888888888888181818183636363636363636363636367272112222222444444444444444488888888888888888181818183636363636363636363636367272
order123334666333334666661212121212121212121212121212121212121212121224662448812121224242424612226664666666664666661212121212121212121212121212121212121212121224662448812121224242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-11-1-1-1111-1-1-1-1-1-11111111111111111111111111111111111111111111111-11-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-111-1-11-1111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-111-1-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11-11-1-1-1-1-111-11111111111111111111111111111111111111111111-1-1-1-1-1-11-11-1-1-1-1-111-11
χ511111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-1-1-1-11111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-1-1-1-111
χ611111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-1
χ711111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1111-111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1111-1
χ811111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1111111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-11
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χ2422-12222-12-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-1-12-1-12-1-1000000-20-200000110122-12222-12-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-1-12-1-12-1-1000000-20-2000001101
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χ2622-12222-12-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-11111-211-211000000-20200000-1-10122-12222-12-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-11111-211-211000000-20200000-1-101
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χ722222-12-1222-1-1-1-122-1-1-1-1222-12-122-1-1-1-122-1-1-1-1-1-1-1-10000-200-20000110010-2-2-2-21-21-2-2-21111-2-21111-2-2-21-21-2-21111-2-211111111000020020000-1-100-10
χ732222-12-1222-1-1-1-1-22-1-1-1-12-2-2-121-22-1-1-1-1-2-2111111110000200-200001100-10-2-2-2-21-21-2-2-211112-21111-2221-2-12-2111122-1-1-1-1-1-1-1-10000-20020000-1-10010
χ742222-12-1222-1-1-1-1-22-1-1-1-12-2-2-121-22-1-1-1-1-2-2111111110000-20020000-1-10010-2-2-2-21-21-2-2-211112-21111-2221-2-12-2111122-1-1-1-1-1-1-1-10000200-200001100-10
χ75222-12222-1-12-1-1-12-12-1-1-1-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-1-102000-1-1-1000000-2-2-21-2-2-2-211-2111-21-2111111-2-2-2-21-211111-2-2111111-2-2110-2000111000000
χ76222-12222-1-12-1-1-12-12-1-1-1-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1-2-2110-2000111000000-2-2-21-2-2-2-211-2111-21-2111111-2-2-2-21-211111-2-211111122-1-102000-1-1-1000000
χ77222-12222-1-12-1-1-1-2-12-1-1-1-11122-2-2-12-1-1-111-2-211111122-1-10-2000-111000000-2-2-21-2-2-2-211-211121-21111-1-1-2-2221-2111-1-122-1-1-1-1-1-1-2-211020001-1-1000000
χ78222-12222-1-12-1-1-1-2-12-1-1-1-11122-2-2-12-1-1-111-2-2111111-2-211020001-1-1000000-2-2-21-2-2-2-211-211121-21111-1-1-2-2221-2111-1-122-1-1-1-1-1-122-1-10-2000-111000000
χ79222-12-222-1-12-1-1-10-12-1-1-11−i3i3-2-2001-2111−i3i300−i3−i3−i3i3i3i32-2-1-1000001−i3i3000000-2-2-21-22-2-211-211101-2111-1i3−i32200-12-1-1-1i3−i300i3i3i3−i3−i3−i3-221100000-1i3−i3000000
χ80222-12-222-1-12-1-1-10-12-1-1-11−i3i3-2-2001-2111−i3i300−i3−i3−i3i3i3i3-221100000-1i3−i3000000-2-2-21-22-2-211-211101-2111-1i3−i32200-12-1-1-1i3−i300i3i3i3−i3−i3−i32-2-1-1000001−i3i3000000
χ81222-12-222-1-12-1-1-10-12-1-1-11i3−i3-2-2001-2111i3−i300i3i3i3−i3−i3−i32-2-1-1000001i3−i3000000-2-2-21-22-2-211-211101-2111-1−i3i32200-12-1-1-1−i3i300−i3−i3−i3i3i3i3-221100000-1−i3i3000000
χ82222-12-222-1-12-1-1-10-12-1-1-11i3−i3-2-2001-2111i3−i300i3i3i3−i3−i3−i3-221100000-1−i3i3000000-2-2-21-22-2-211-211101-2111-1−i3i32200-12-1-1-1−i3i300−i3−i3−i3i3i3i32-2-1-1000001i3−i3000000
χ8322-12222-12-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-1-12-1-12-1-100000020200000-1-10-1-2-21-2-2-2-21-211-211-211-211-2-2-2-21-2111-2111111-211-211000000-20-2000001101
χ8422-12222-12-1-12-1-12-1-12-1-12222-12-1-1-12-1-1-1-1-1-12-1-12-1-1000000-20-2000001101-2-21-2-2-2-21-211-211-211-211-2-2-2-21-2111-2111111-211-21100000020200000-1-10-1
χ8522-12222-12-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-11111-211-21100000020-200000110-1-2-21-2-2-2-21-211-211211-211-222-212-111-211-1-1-1-12-1-12-1-1000000-20200000-1-101
χ8622-12222-12-1-12-1-1-2-1-12-1-12-2-22-1-21-1-12-1-11111-211-211000000-20200000-1-101-2-21-2-2-2-21-211-211211-211-222-212-111-211-1-1-1-12-1-12-1-100000020-200000110-1
χ874444-2-4-2444-2-2-2-204-2-2-2-2-4002-400-422220000000000000000000000000000-4-4-4-4242-4-4-422220-42222400-24004-2-2-2-20000000000000000000000000000
χ88444-2-24-24-2-2-21114-2-2111-2-2-2-24-24-2-2111-2-2-2-2111111000000000000000000-4-4-422-42-4222-1-1-1-422-1-1-12222-42-422-1-1-12222-1-1-1-1-1-1000000000000000000
χ89444-2-24-24-2-2-2111-4-2-2111-222-242-4-2-21112222-1-1-1-1-1-1000000000000000000-4-4-422-42-4222-1-1-1422-1-1-12-2-22-4-2422-1-1-1-2-2-2-2111111000000000000000000
χ90444-2-2-4-24-2-2-21110-2-21112−2i32i32-40022-1-1-1−2i32i300i3i3i3−i3−i3−i3000000000000000000-4-4-42242-4222-1-1-1022-1-1-1-22i3−2i3-2400-2-21112i3−2i300−i3−i3−i3i3i3i3000000000000000000
χ91444-2-2-4-24-2-2-21110-2-211122i3−2i32-40022-1-1-12i3−2i300−i3−i3−i3i3i3i3000000000000000000-4-4-42242-4222-1-1-1022-1-1-1-2−2i32i3-2400-2-2111−2i32i300i3i3i3−i3−i3−i3000000000000000000
χ9244-244-44-24-2-24-2-20-2-24-2-2-400-420022-4220000000000000000000000000000-4-42-4-44-42-422-422022-4224004-200-2-24-2-20000000000000000000000000000
χ9344-24-24-2-24-21-2114-21-211444-2-2-2-2-21-211-2-211-211-211000000000000000000-4-42-42-422-42-12-1-1-42-12-1-1-4-4-422222-12-1-122-1-12-1-12-1-1000000000000000000
χ9444-24-24-2-24-21-211-4-21-2114-4-4-2-222-21-21122-1-12-1-12-1-1000000000000000000-4-42-42-422-42-12-1-142-12-1-1-44422-2-22-12-1-1-2-211-211-211000000000000000000
χ9544-24-2-4-2-24-21-2110-21-211-40022002-12-1-1003-303-303-3000000000000000000-4-42-42422-42-12-1-102-12-1-1400-2-200-21-21100-330-330-33000000000000000000
χ9644-24-2-4-2-24-21-2110-21-211-40022002-12-1-100-330-330-33000000000000000000-4-42-42422-42-12-1-102-12-1-1400-2-200-21-211003-303-303-3000000000000000000
χ9744-2-2444-2-21-2-21141-2-211-2-2-24-24-21-2-21111-2-2-211-211000000000000000000-4-422-4-4-422-122-1-1-4-122-1-1222-42-42-122-1-1-1-1222-1-12-1-1000000000000000000
χ9844-2-2444-2-21-2-211-41-2-211-2224-2-421-2-211-1-1222-1-12-1-1000000000000000000-4-422-4-4-422-122-1-14-122-1-12-2-2-424-2-122-1-111-2-2-211-211000000000000000000
χ9944-2-24-44-2-21-2-21101-2-2112−2i32i3-4200-122-1-1i3−i300−2i3i3i32i3−i3−i3000000000000000000-4-422-44-422-122-1-10-122-1-1-22i3−2i34-2001-2-211−i3i3002i3−i3−i3−2i3i3i3000000000000000000
χ10044-2-24-44-2-21-2-21101-2-21122i3−2i3-4200-122-1-1−i3i3002i3−i3−i3−2i3i3i3000000000000000000-4-422-44-422-122-1-10-122-1-1-2−2i32i34-2001-2-211i3−i300−2i3i3i32i3−i3−i3000000000000000000
χ10144-2-2-24-2-2-2111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2-2-2-2-2111−1−3i32−1+3i3211111−1−3i32−1+3i321−1+3i32−1−3i32000000000000000000-4-4222-4222-1-1-11+3i321−3i32-4-1-1-11+3i321−3i322222222-1-1-11+3i321−3i32-1-1-1-1-11+3i321−3i32-11−3i321+3i32000000000000000000
χ10244-2-2-24-2-2-2111−1−3i32−1+3i32-4111−1−3i32−1+3i32-222-2-222111−1−3i32−1+3i32-1-1-1-1-11+3i321−3i32-11−3i321+3i32000000000000000000-4-4222-4222-1-1-11+3i321−3i324-1-1-11+3i321−3i322-2-222-2-2-1-1-11+3i321−3i3211111−1−3i32−1+3i321−1+3i32−1−3i32000000000000000000
χ10344-2-2-24-2-2-2111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2-2-2-2-2111−1+3i32−1−3i3211111−1+3i32−1−3i321−1−3i32−1+3i32000000000000000000-4-4222-4222-1-1-11−3i321+3i32-4-1-1-11−3i321+3i322222222-1-1-11−3i321+3i32-1-1-1-1-11−3i321+3i32-11+3i321−3i32000000000000000000
χ10444-2-2-24-2-2-2111−1+3i32−1−3i32-4111−1+3i32−1−3i32-222-2-222111−1+3i32−1−3i32-1-1-1-1-11−3i321+3i32-11+3i321−3i32000000000000000000-4-4222-4222-1-1-11−3i321+3i324-1-1-11−3i321+3i322-2-222-2-2-1-1-11−3i321+3i3211111−1+3i32−1−3i321−1−3i32−1+3i32000000000000000000
χ10544-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i322−2i32i32200-1-1-11+3i321−3i32i3−i33-3i3−3−i323−i32−i3−3+i323+i32000000000000000000-4-42224222-1-1-11+3i321−3i320-1-1-11+3i321−3i32-22i3−2i3-2-200111−1−3i32−1+3i32−i3i3-33−i33+i32−3+i32i33−i32−3−i32000000000000000000
χ10644-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i3222i3−2i32200-1-1-11+3i321−3i32−i3i3-33−i33+i32−3+i32i33−i32−3−i32000000000000000000-4-42224222-1-1-11+3i321−3i320-1-1-11+3i321−3i32-2−2i32i3-2-200111−1−3i32−1+3i32i3−i33-3i3−3−i323−i32−i3−3+i323+i32000000000000000000
χ10744-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i322−2i32i32200-1-1-11−3i321+3i32i3−i3-33i33−i32−3−i32−i33+i32−3+i32000000000000000000-4-42224222-1-1-11−3i321+3i320-1-1-11−3i321+3i32-22i3−2i3-2-200111−1+3i32−1−3i32−i3i33-3−i3−3+i323+i32i3−3−i323−i32000000000000000000
χ10844-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i3222i3−2i32200-1-1-11−3i321+3i32−i3i33-3−i3−3+i323+i32i3−3−i323−i32000000000000000000-4-42224222-1-1-11−3i321+3i320-1-1-11−3i321+3i32-2−2i32i3-2-200111−1+3i32−1−3i32i3−i3-33i33−i32−3−i32−i33+i32−3+i32000000000000000000
χ1094-44440-4-4-4444440-4-4-4-4-40000000000000000000000000000000000000000-44-4-4-40444-4-4-4-4-40444440000000000000000000000000000000000000000
χ1104-444-202-4-44-2-2-2-20-4222200000000000000000000000000000000006−60000-44-4-420-244-4222204-2-2-2-20000000000000000000000000000000000−660000
χ1114-444-202-4-44-2-2-2-20-422220000000000000000000000000000000000−660000-44-4-420-244-4222204-2-2-2-200000000000000000000000000000000006−60000
χ1124-44-240-4-42-24-2-2-202-4222000000000000000000000000−2i32i300000000000000-44-42-4044-22-42220-24-2-2-20000000000000000000000002i3−2i300000000000000
χ1134-44-240-4-42-24-2-2-202-42220000000000000000000000002i3−2i300000000000000-44-42-4044-22-42220-24-2-2-2000000000000000000000000−2i32i300000000000000
χ1144-4-2440-42-4-2-24-2-2022-422000000000000000000000000000000000000i6−i600-442-4-404-2422-4220-2-24-2-2000000000000000000000000000000000000−i6i600
χ1154-4-2440-42-4-2-24-2-2022-422000000000000000000000000000000000000−i6i600-442-4-404-2422-4220-2-24-2-2000000000000000000000000000000000000i6−i600
χ1168-88-4-404-84-4-4222044-2-2-20000000000000000000000000000000000000000-88-8440-48-444-2-2-20-4-42220000000000000000000000000000000000000000
χ1178-8-48-4044-8-42-42204-24-2-20000000000000000000000000000000000000000-884-840-4-484-24-2-20-42-4220000000000000000000000000000000000000000
χ1188-8-4-480-8442-4-4220-244-2-20000000000000000000000000000000000000000-8844-808-4-4-244-2-202-4-4220000000000000000000000000000000000000000
χ1198-8-4-4-40444222−1−3i3−1+3i30-2-2-21+3i31−3i30000000000000000000000000000000000000000-884440-4-4-4-2-2-21+3i31−3i30222−1−3i3−1+3i30000000000000000000000000000000000000000
χ1208-8-4-4-40444222−1+3i3−1−3i30-2-2-21−3i31+3i30000000000000000000000000000000000000000-884440-4-4-4-2-2-21−3i31+3i30222−1+3i3−1−3i30000000000000000000000000000000000000000

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