Finite Group Databasebeta

← Group #13139933

Character table — Group #13139933

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111222222446666666666661212121212121212121218181818181818181818181836363636363636363636363611112222224466666666666612121212121212121212181818181818181818181818363636363636363636363636
order1222344666121233666666121212123666121212121212888824242424242424244444121212121212121222226446661212666666661212121266661212121212128888242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
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χ61-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ71-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii
χ81-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1-11-11-11-11-11-111-1-1-111-1-1-1111-1-111-111-1-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−i
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χ102222222222222-122-12-1-12222-1-1-1-1-1-1-1-1-1-100000000000000-2-2000011112222222222222-122-12-1-12222-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111
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χ7822-2-22002-2-200-12-1121-2-23−33−3-1-111003−33−32−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000-2-222-200-222001-21-1-2-122−33−3311-1-100−33−33−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ7922-2-22002-2-200-12-1121-2-23−33−3-1-111003−33−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000-2-222-200-222001-21-1-2-122−33−3311-1-100−33−332−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ8022-2-22002-2-200-12-1121-2-2−33−33-1-11100−33−332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000-2-222-200-222001-21-1-2-1223−33−311-1-1003−33−3−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ8122-2-22002-2-200-12-1121-2-2−33−33-1-11100−33−33−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000-2-222-200-222001-21-1-2-1223−33−311-1-1003−33−32−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ822-22-222-2-22-2-2222-2-2-222-222-2-22-2-22-22-2-222000000000000000000000000-22-22-2-222-222-2-2-2222-2-22-2-222-222-22-222-2-2000000000000000000000000
χ832-22-222-2-22-2-222-1-2-212-1122-2-2-111-11-111-1-1000000000000000000003−3−33-22-22-2-222-222-2-2122-1-21-1-2-2221-1-11-11-1-11100000000000000000000−333−3
χ842-22-222-2-22-2-222-1-2-212-1122-2-2-111-11-111-1-100000000000000000000−333−3-22-22-2-222-222-2-2122-1-21-1-2-2221-1-11-11-1-111000000000000000000003−3−33
χ852-22-222-2-22-2-22-1211-2-12-2-1-111-111-1-2211-1-1000033−3−3−3−333000000000000-22-22-2-222-222-21-2-1-121-2211-1-11-1-112-2-1-1110000−3−33333−3−3000000000000
χ862-22-222-2-22-2-22-1211-2-12-2-1-111-111-1-2211-1-10000−3−33333−3−3000000000000-22-22-2-222-222-21-2-1-121-2211-1-11-1-112-2-1-111000033−3−3−3−333000000000000
χ872-22-22-22-22-22-22-1-2-212-11-2-222-111-1-11-1-111000000000000002i−2i0000−i−iii-22-22-22-22-22-22-2122-1-21-122-2-21-1-111-111-1-100000000000000−2i2i0000ii−i−i
χ882-22-22-22-22-22-22-1-2-212-11-2-222-111-1-11-1-11100000000000000−2i2i0000ii−i−i-22-22-22-22-22-22-2122-1-21-122-2-21-1-111-111-1-1000000000000002i−2i0000−i−iii
χ892-22-22-22-22-22-2-1211-2-12-211-1-1-111-12-2-1-11122-2-2-1-1-1-11111000000000000-22-22-22-22-22-221-2-1-121-22-1-1111-1-11-2211-1-1-2-2221111-1-1-1-1000000000000
χ902-22-22-22-22-22-2-1211-2-12-211-1-1-111-12-2-1-111-2-2221111-1-1-1-1000000000000-22-22-22-22-22-221-2-1-121-22-1-1111-1-11-2211-1-122-2-2-1-1-1-11111000000000000
χ912-2-22200-2-220022-22-2-2-2200002-22-20000002−2−222−22−2−22−22000000000000-222-2-20022-200-2-22-2222-20000-22-22000000−222−2−22−222−22−2000000000000
χ922-2-22200-2-220022-22-2-2-2200002-22-2000000−222−2−22−222−22−2000000000000-222-2-20022-200-2-22-2222-20000-22-220000002−2−222−22−2−22−22000000000000
χ932-2-22200-2-2200-121-1-21-223−3−33-11-1100−333−32−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000-222-2-20022-2001-2-112-12-2−333−31-11-1003−3−33−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ942-2-22200-2-2200-121-1-21-223−3−33-11-1100−333−3−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000-222-2-20022-2001-2-112-12-2−333−31-11-1003−3−332−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ952-2-22200-2-2200-121-1-21-22−333−3-11-11003−3−332−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000-222-2-20022-2001-2-112-12-23−3−331-11-100−333−3−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ962-2-22200-2-2200-121-1-21-22−333−3-11-11003−3−33−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000-222-2-20022-2001-2-112-12-23−3−331-11-100−333−32−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ97444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-21111000000000000000000000000-4-4-4-4-4-4-4-4-4-4-4-4222222222222-1-1-1-122-1-1-1-1000000000000000000000000
χ9844444-4-4444-4-4-2-2-2-2-2-2-2-22222111122-1-1-1-1000000000000000000000000-4-4-4-4-444-4-4-44422222222-2-2-2-2-1-1-1-1-2-21111000000000000000000000000
χ9944-4-44004-4-4004-24-4-2-4220000-2-222000000000000000000000000000000-4-444-400-44400-42-4424-2-2000022-2-2000000000000000000000000000000
χ10044-4-44004-4-400-2-2-22-222223−2323−2311-1-100−33−33000000000000000000000000-4-444-400-44400222-22-2-2-2−2323−2323-1-111003−33−3000000000000000000000000
χ10144-4-44004-4-400-2-2-22-2222−2323−232311-1-1003−33−3000000000000000000000000-4-444-400-44400222-22-2-2-223−2323−23-1-11100−33−33000000000000000000000000
χ1024-44-444-4-44-4-44-2-2222-2-22-2-2221-1-112-2-1-111000000000000000000000000-44-44-4-444-444-422-2-2-222-222-2-2-111-1-2211-1-1000000000000000000000000
χ1034-44-44-44-44-44-4-2-2222-2-2222-2-21-1-11-2211-1-1000000000000000000000000-44-44-44-44-44-4422-2-2-222-2-2-222-111-12-2-1-111000000000000000000000000
χ1044-4-44400-4-44004-2-442-42-20000-22-22000000000000000000000000000000-444-4-40044-400-424-4-24-2200002-22-2000000000000000000000000000000
χ1054-4-44400-4-4400-2-22-2222-223−23−23231-11-1003−3−33000000000000000000000000-444-4-40044-40022-22-2-2-22−232323−23-11-1100−333−3000000000000000000000000
χ1064-4-44400-4-4400-2-22-2222-2−232323−231-11-100−333−3000000000000000000000000-444-4-40044-40022-22-2-2-2223−23−2323-11-11003−3−33000000000000000000000000
χ1076666-366-3-3-3-3-300000000000000000000000000000000002200-1-1-1-10000-6-6-6-63-6-6333330000000000000000000000000000000000-2-20011110000
χ1086666-366-3-3-3-3-30000000000000000000000000000000000-2-20011110000-6-6-6-63-6-63333300000000000000000000000000000000002200-1-1-1-10000
χ1096666-3-6-6-3-3-33300000000000000000000000000000000000000−i3i3−i3i30000-6-6-6-6366333-3-300000000000000000000000000000000000000i3−i3i3−i30000
χ1106666-3-6-6-3-3-33300000000000000000000000000000000000000i3−i3i3−i30000-6-6-6-6366333-3-300000000000000000000000000000000000000−i3i3−i3i30000
χ1116-66-6-36-63-333-3000000000000000000000000000000000000003−3−330000-66-663-66-33-3-3300000000000000000000000000000000000000−333−30000
χ1126-66-6-36-63-333-300000000000000000000000000000000000000−333−30000-66-663-66-33-3-33000000000000000000000000000000000000003−3−330000
χ1136-66-6-3-663-33-3300000000000000000000000000000000002i−2i00−i−iii0000-66-6636-6-33-33-30000000000000000000000000000000000−2i2i00ii−i−i0000
χ1146-66-6-3-663-33-330000000000000000000000000000000000−2i2i00ii−i−i0000-66-6636-6-33-33-300000000000000000000000000000000002i−2i00−i−iii0000
χ1151212-12-12-600-666000000000000000000000000000000000000000000000000-12-1212126006-6-6000000000000000000000000000000000000000000000000
χ11612-12-1212-60066-6000000000000000000000000000000000000000000000000-121212-12600-6-66000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.