Finite Group Databasebeta

← Group #13138804

Character table — Group #13138804

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order122234466688881212121224242424242424243366666636661212121212121212242424242424242424242424242424244444888812121212121212122424242424242424222266666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-122-1-12-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ10222222222222222222222222222-122-1-12-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ1122222222222222222222222222-12-1-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ1222222222222222222222222222-12-1-122-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000002-20000-1-111
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-1-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100000000000000000000000000-22000011-1-1
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-2111111110000000000000000000000002-200-1-1110000
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000000000000000000000000-220011-1-10000
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χ2022-2-222-22-2-222-2-222-2-22222-2-2-2-22-1-2-2112-1-111-1-21112-1-1-122-2-2-1-111-1-1-1-1111100000000000000000000000000000000−i3i3−i3i3
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χ2222-2-222-22-2-222-2-222-2-22222-2-2-2-2-1211-2-2-12-111-11-211-12-1-1-1-11122-2-2-1-1-1-111110000000000000000000000000000−i3i3−i3i30000
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χ2822-2-222-22-2-2-2-22222-2-2-2-2-2-22222-1211-2-2-12-111-11-211-12-1-111-1-1-2-2221111-1-1-1-10000000000000000000000000000i3−i3−i3i30000
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χ332-22-2200-22-2−22−220000−2−222−2−222222-22-2-2-222-2-200000000−22−22−22−22−2−222−2−222002-2−22−22000022-2-2−2−222−2−222000000000000
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χ906-66-6-3003-33−3232−3232−3333−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ700000000000000000000000000000000000000-222−22−2−333−311-1-1ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ916-6-66-30033-332−32−323233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002-2002−2−22-1-1113−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ926-6-66-30033-332−32−323233−33−33333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000-2200−222−211-1-1−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ936-6-66-30033-332−32−3232−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002-2002−2−22-1-111−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ946-6-66-30033-332−32−3232−333333−333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000-2200−222−211-1-13−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ956-6-66-30033-3−323232−3233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002-200−222−2-1-1113−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ966-6-66-30033-3−323232−3233−33−3333−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000-22002−2−2211-1-1−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ976-6-66-30033-3−323232−32−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002-200−222−2-1-111−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ986-6-66-30033-3−323232−32−333333−33−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000-22002−2−2211-1-13−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000

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