Finite Group Databasebeta

← Group #13138792

Character table — Group #13138792

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order1222344666888812121212242424242424242433666666444436661212121212121212242424242424242424242424242424244488881212121212121212242424242424242422224444666612121212
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
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ911-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-1-111-1ii−i−i1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i
χ1011-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-1-111-1ii−i−i1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii
χ1111-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-1-111-1−i−iii1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii
χ1211-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-1-111-1−i−iii1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i
χ1311-1-111-11-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1ii−i−i1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ1411-1-111-11-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1ii−i−i1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ1511-1-111-11-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1−i−iii1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ1611-1-111-11-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1−i−iii1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
χ17222222222222222222222222222-12-1-12-120000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000022220000-1-1-1-10000
χ18222222222222222222222222222-12-1-12-120000-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000-2-2-2-2000011110000
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χ212222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-12-120000-1-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000000022-2-20000-1-1110000
χ222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-12-120000-1-1-1-12-1-1-12-1-1-1-2-2111111-2-21111110000000000000000000000-2-222000011-1-10000
χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-10000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-211110000000000000000000000000022-2-20000-1-111
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-10000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-2111100000000000000000000000000-2-222000011-1-1
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χ2822-2-222-22-2-222-2-222-2-22222-2-2-2-22-1-2112-1-20000-111-1-21112-1-1-122-1-1-1-1-1-1-2-21111110000000000000000000000-22-2200001-11-10000
χ2922-2-222-22-2-222-2-222-2-22222-2-2-2-2-121-2-2-1210000-111-11-211-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000002i−2i2i−2i0000−ii−ii
χ3022-2-222-22-2-222-2-222-2-22222-2-2-2-2-121-2-2-1210000-111-11-211-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000000000−2i2i−2i2i0000i−ii−i
χ3122-2-222-22-2-2-2-22222-2-2-2-2-2-222222-1-2112-1-20000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000002-2-220000-111-10000
χ3222-2-222-22-2-2-2-22222-2-2-2-2-2-222222-1-2112-1-20000-111-1-21112-1-1-1-2-211111122-1-1-1-1-1-10000000000000000000000-222-200001-1-110000
χ3322-2-222-22-2-2-2-22222-2-2-2-2-2-22222-121-2-2-1210000-111-11-211-12-1-111-2-21111-1-122-1-1-1-1000000000000000000000000002i−2i−2i2i0000−iii−i
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χ442-2-22200-2-22−222−20000−2−22222−2−222-2-22-2-22-222-22-22-200000000−22−22−2−2222−22−222−2−200−222−2-22002-200−2−22222−2−20000000000000000
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χ896-66-6-3003-3332−3232−3233−3333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000002i−2i2i−2i000000000000000000000000000000−i2i2−i2i2−ii−i3i3−ii−i3i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ906-66-6-3003-3332−3232−3233−3333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ2300000000−2i2i−2i2i000000000000000000000000000000i2−i2i2−i2i−ii3−i3i−ii3−i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ916-66-6-3003-3332−3232−32−3333−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000002i−2i2i−2i000000000000000000000000000000−i2i2−i2i2−iii3−i3−iii3−i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ926-66-6-3003-3332−3232−32−3333−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ700000000−2i2i−2i2i000000000000000000000000000000i2−i2i2−i2i−i−i3i3i−i−i3i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ936-66-6-3003-33−3232−323233−3333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000002i−2i2i−2i000000000000000000000000000000i2−i2i2−i2−ii−i3i3−ii−i3i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ946-66-6-3003-33−3232−323233−3333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ2300000000−2i2i−2i2i000000000000000000000000000000−i2i2−i2i2i−ii3−i3i−ii3−i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ956-66-6-3003-33−3232−3232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000002i−2i2i−2i000000000000000000000000000000i2−i2i2−i2−iii3−i3−iii3−i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ966-66-6-3003-33−3232−3232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000−2i2i−2i2i000000000000000000000000000000−i2i2−i2i2i−i−i3i3i−i−i3i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ976-6-66-30033-332−32−323233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000002-2-22000000000000000000000000000000−222−2-11−331-13−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ986-6-66-30033-332−32−323233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ2300000000-222-20000000000000000000000000000002−2−221-13−3-11−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ996-6-66-30033-332−32−3232−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000002-2-22000000000000000000000000000000−222−2-113−31-1−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ1006-6-66-30033-332−32−3232−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000-222-20000000000000000000000000000002−2−221-1−33-113−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ1016-6-66-30033-3−323232−3233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000002-2-220000000000000000000000000000002−2−22-11−331-13−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ1026-6-66-30033-3−323232−3233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ2300000000-222-2000000000000000000000000000000−222−21-13−3-11−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ1036-6-66-30033-3−323232−32−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000002-2-220000000000000000000000000000002−2−22-113−31-1−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ1046-6-66-30033-3−323232−32−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ700000000-222-2000000000000000000000000000000−222−21-1−33-113−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000

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