Finite Group Databasebeta

← Group #13138942

Character table — Group #13138942

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order122234466688881212121224242424242424243366666636661212121212121212242424242424242424242424242424242244666688881212121224242424242424242244666612121212
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
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-1-12-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ10222222222222222222222222222-12-1-12-12-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ1122222222222222222222222222-12-122-12-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ1222222222222222222222222222-12-122-12-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ132222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-12-12-1-1-1-12-1-1-12-1-1-1-2-2-2-21111111111110000000000000000000000002-200-1-1110000
χ142222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-12-12-1-1-1-12-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000-220011-1-10000
χ152222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000000000000000000000000002-20000-1-111
χ162222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-1-1-1-1-1-12-1-1-12-1-11111-2-2-2-21111111100000000000000000000000000-22000011-1-1
χ1722222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2-2-200000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
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χ252-22-22-22-2-222-22-2-2-22222-2-222-2-222-2-2-222-22-2-22-2-2-2-222222-22-22-22-222-2-222-2-2000000000000000000000000000000000000
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χ282-22-22-22-2-222-22-2-2-22222-2-222-2-2-121-2-2-121-111-11-211-12-1-1-11-112-22-2-1-111-1-111000000000000000000000000000000003−33−3
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χ302-22-22-22-2-22-22-22-2-222-2-222-2-22222-2-2-222-22-2-22-2-2-2-22222-22-22-22-22-2-222-2-222000000000000000000000000000000000000
χ312-22-22-22-2-22-22-22-2-222-2-222-2-2222-1-2112-1-2-111-1-21112-1-1-1-22-221-11-111-1-111-1-10000000000000000000000000000−i3i3i3−i30000
χ322-22-22-22-2-22-22-22-2-222-2-222-2-2222-1-2112-1-2-111-1-21112-1-1-1-22-221-11-111-1-111-1-10000000000000000000000000000i3−i3−i3i30000
χ332-22-22-22-2-22-22-22-2-222-2-222-2-222-121-2-2-121-111-11-211-12-1-11-11-1-22-2211-1-111-1-1000000000000000000000000000000003−3−33
χ342-22-22-22-2-22-22-22-2-222-2-222-2-222-121-2-2-121-111-11-211-12-1-11-11-1-22-2211-1-111-1-100000000000000000000000000000000−333−3
χ352-2-22200-22-22−2−22000022−2−2−2−22222-2-22-2-222-22-2000000002−2−222−2−2222−2−2−2−2222-20022-2-22−2−22000022−2−2−2−222000000000000
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χ876-66-6-3-6633-36-66-633-3-3-3-333-3-3330000000000000000000000000000000000000000−i3i3i3−i30000i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000
χ886-66-6-3-6633-36-66-633-3-3-3-333-3-3330000000000000000000000000000000000000000i3−i3−i3i30000−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000
χ896-66-6-3-6633-3-66-6633-3-333-3-333-3-30000000000000000000000000000000000000000−i3i3i3−i30000i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ906-66-6-3-6633-3-66-6633-3-333-3-333-3-30000000000000000000000000000000000000000i3−i3−i3i30000−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ916-6-66-3003-3332−32−323233−33−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ70000000000000000000000000000000000002-200-1-1112−2−223−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ926-6-66-3003-3332−32−323233−33−33333ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ7000000000000000000000000000000000000-220011-1-1−222−2−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ936-6-66-3003-3332−32−3232−333333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ230000000000000000000000000000000000002-200-1-1112−2−22−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ946-6-66-3003-3332−32−3232−333333−333ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ23000000000000000000000000000000000000-220011-1-1−222−23−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ956-6-66-3003-33−323232−3233−33−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ70000000000000000000000000000000000002-200-1-111−222−23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ966-6-66-3003-33−323232−3233−33−3333−3ζ13+3ζ23−3ζ5+3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ7−3ζ13+3ζ23−3ζ5+3ζ7000000000000000000000000000000000000-220011-1-12−2−22−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ976-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ230000000000000000000000000000000000002-200-1-111−222−2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ986-6-66-3003-33−323232−32−333333−33−3ζ5+3ζ7−3ζ13+3ζ233ζ5−3ζ73ζ13−3ζ233ζ5−3ζ73ζ13−3ζ23−3ζ5+3ζ7−3ζ13+3ζ23000000000000000000000000000000000000-220011-1-12−2−223−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000

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