Finite Group Databasebeta

← Group #13138908

Character table — Group #13138908

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order1222344666888812121212242424242424242433666666222236661212121212121212242424242424242424242424242424244466668888121212122424242424242424444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ91-11-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i
χ101-11-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii
χ111-11-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-11111i−ii−i−ii−iii−ii−i−ii−ii
χ121-11-11-11-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-11111−ii−iii−ii−i−ii−iii−ii−i
χ131-11-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii
χ141-11-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i
χ151-11-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-1111111-1-1-1-1i−i−ii−iii−ii−i−ii−iii−i
χ161-11-11-11-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-1111111-1-1-1-1−iii−ii−i−ii−iii−ii−i−ii
χ17222222222222222222222222222-12-12-12-10000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000000022220000-1-1-1-1
χ18222222222222222222222222222-12-12-12-10000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000000-2-2-2-200001111
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χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-12-12-120000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000022-2-20000-1-1110000
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χ332-22-22-22-2-2222-2-2-2-2222222-2-2-2-22-1-212-1-210000-111-1-21112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000000002i−2i2i−2i0000−ii−ii
χ342-22-22-22-2-2222-2-2-2-2222222-2-2-2-22-1-212-1-210000-111-1-21112-1-1-122-1-1-1-1-1-1-2-211111100000000000000000000000000−2i2i−2i2i0000i−ii−i
χ352-22-22-22-2-2222-2-2-2-2222222-2-2-2-2-121-2-121-20000-111-11-211-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000002i−2i2i−2i0000−ii−ii0000
χ362-22-22-22-2-2222-2-2-2-2222222-2-2-2-2-121-2-121-20000-111-11-211-12-1-1-1-122-1-1-1-111-2-211110000000000000000000000−2i2i−2i2i0000i−ii−i0000
χ372-22-22-22-2-22-2-222-2-222-2-2-2-222222-1-212-1-210000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-1000000000000000000000000002i−2i−2i2i0000−iii−i
χ382-22-22-22-2-22-2-222-2-222-2-2-2-222222-1-212-1-210000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000−2i2i2i−2i0000i−i−ii
χ392-22-22-22-2-22-2-222-2-222-2-2-2-22222-121-2-121-20000-111-11-211-12-1-111-2-21111-1-122-1-1-1-100000000000000000000002i−2i−2i2i0000−iii−i0000
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χ412-2-22200-22-22−2−22000022−2−2−2−22222-2-2-2-2222-2-222-22-2000000002−22−222−2−2−22−22−2−222002-2-222−2−22000022−2−2−2−2220000000000000000
χ422-2-22200-22-22−2−22000022−2−2−2−22222-2-2-2-222-222-22-22-2000000002−22−222−2−2−22−22−2−22200-222-2−222−20000−2−22222−2−20000000000000000
χ432-2-22200-22-2−222−20000−2−22222−2−222-2-2-2-2222-2-222-22-200000000−22−22−2−2222−22−222−2−2002-2-22−222−20000−2−22222−2−20000000000000000
χ442-2-22200-22-2−222−20000−2−22222−2−222-2-2-2-222-222-22-22-200000000−22−22−2−2222−22−222−2−200-222-22−2−22000022−2−2−2−2220000000000000000
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χ8666-6-6-300-333−3232−323233−3333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ2300000000-22-220000000000000000000000000000001-11-12−22−2−33−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ8766-6-6-300-333−3232−3232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000002-22-2000000000000000000000000000000-11-11−22−22−33−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ8866-6-6-300-333−3232−3232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000-22-220000000000000000000000000000001-11-12−22−23−33−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ896-66-6-36-633-30000-3-33333−3333−33−3333−33330000000022-2-20000000000000000000000000000-22-1-111000011-1-13−33−3−33−330000000000000000
χ906-66-6-36-633-30000-3-33333−3333−33−3333−333300000000-2-22200000000000000000000000000002-211-1-10000-1-111−33−333−33−30000000000000000
χ916-66-6-36-633-30000-3-333−3333−333333−3333−330000000022-2-20000000000000000000000000000-22-1-111000011-1-1−33−333−33−30000000000000000
χ926-66-6-36-633-30000-3-333−3333−333333−3333−3300000000-2-22200000000000000000000000000002-211-1-10000-1-1113−33−3−33−330000000000000000
χ936-66-6-3-6633-366-6-633-3-3-3-3-3-333330000000022-2-200000000000000000000000000002-2-1-11122-2-2-1-111-1-1-1-111110000000000000000
χ946-66-6-3-6633-366-6-633-3-3-3-3-3-3333300000000-2-2220000000000000000000000000000-2211-1-1-2-22211-1-11111-1-1-1-10000000000000000
χ956-66-6-3-6633-3-6-66633-3-33333-3-3-3-30000000022-2-200000000000000000000000000002-2-1-111-2-222-1-1111111-1-1-1-10000000000000000
χ966-66-6-3-6633-3-6-66633-3-33333-3-3-3-300000000-2-2220000000000000000000000000000-2211-1-122-2-211-1-1-1-1-1-111110000000000000000
χ976-6-66-3003-3332−32−323233−33−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000002-2-22000000000000000000000000000000-111-12−2−22−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ986-6-66-3003-3332−32−323233−33−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000-222-20000000000000000000000000000001-1-11−222−23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ996-6-66-3003-3332−32−3232−333333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000002-2-22000000000000000000000000000000-111-12−2−223−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ1006-6-66-3003-3332−32−3232−333333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ2300000000-222-20000000000000000000000000000001-1-11−222−2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ1016-6-66-3003-33−323232−3233−33−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000002-2-22000000000000000000000000000000-111-1−222−2−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ1026-6-66-3003-33−323232−3233−33−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ700000000-222-20000000000000000000000000000001-1-112−2−223−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ1036-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000002-2-22000000000000000000000000000000-111-1−222−23−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ1046-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ2300000000-222-20000000000000000000000000000001-1-112−2−22−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000

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