Finite Group Databasebeta

← Group #13141261

Character table — Group #13141261

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111333344444466666666612121212121212121212121212121212121212121212242424242424242424484848484848484848484848484848484848484848484848
order12336633664412121212266666666246666666612121212121212121212121241212121212121212333333666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ41111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32
χ61111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32
χ7111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ8111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32
χ9111111−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211
χ10111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ11111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i321+i321+i321−i321−i32-1-11−i321−i32-1-11+i321+i32
χ12111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211−i321−i32-1-11+i321+i321+i321+i321−i321−i32-1-1
χ13111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ14111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211
χ15111111−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32
χ16111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ17111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211+i321+i32-1-11−i321−i321−i321−i321+i321+i32-1-1
χ18111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i321−i321−i321+i321+i32-1-11+i321+i32-1-11−i321−i32
χ193333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1000000000000000000000000
χ203333333333-3-3-3-3-3-3333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3111111111000000000000000000000000
χ21333333−3−3i32−3+3i32−3−3i32−3+3i32333333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321+i321−i321−i321−i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000000000000000
χ22333333−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-3-3-3333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321+i321−i321−i321−i323+3i323+3i323−3i323−3i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000000000000000
χ23333333−3+3i32−3−3i32−3+3i32−3−3i32333333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321−i321+i321+i321+i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-11−i321−i321−i321+i321+i321+i32000000000000000000000000
χ24333333−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-3-3-3333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321−i321+i321+i321+i323−3i323−3i323+3i323+3i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000000000000
χ2533−3−3i32−3+3i32−3−3i32−3+3i32000033−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i3200000033−3−3i32−3+3i32000000−3−3i32−3+3i3200000000003−3−3i32−3+3i32000000000000000000000000000000
χ2633−3−3i32−3+3i32−3−3i32−3+3i32000033−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i32000000-1-11+i321−i322−1−i3−1+i32−1−i3−1+i31+i321−i322−1−i3−1+i32−1−i3−1+i30000-11+i321−i322−1−i3−1+i32−1−i3−1+i3000000000000000000000000
χ2733−3−3i32−3+3i32−3−3i32−3+3i32000033−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i32000000-1-11+i321−i32−1−i3−1+i32−1+i32−1−i31+i321−i32−1−i3−1+i32−1+i32−1−i30000-11+i321−i32−1−i3−1+i32−1+i32−1−i3000000000000000000000000
χ2833−3−3i32−3+3i32−3−3i32−3+3i32000033−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i32000000-1-11+i321−i32−1+i32−1−i3−1−i3−1+i321+i321−i32−1+i32−1−i3−1−i3−1+i320000-11+i321−i32−1+i32−1−i3−1−i3−1+i32000000000000000000000000
χ2933−3−3i32−3+3i32−3−3i32−3+3i320000-3-33+3i323+3i323−3i323−3i323−3−3i32−3+3i3200000033−3−3i32−3+3i32000000−3−3i32−3+3i320000000000-33+3i323−3i32000000000000000000000000000000
χ3033−3−3i32−3+3i32−3−3i32−3+3i320000-3-33+3i323+3i323−3i323−3i323−3−3i32−3+3i32000000-1-11+i321−i322−1−i3−1+i32−1−i3−1+i31+i321−i322−1−i3−1+i32−1−i3−1+i300001−1−i32−1+i32-21+i31−i3-21+i31−i3000000000000000000000000
χ3133−3−3i32−3+3i32−3−3i32−3+3i320000-3-33+3i323+3i323−3i323−3i323−3−3i32−3+3i32000000-1-11+i321−i32−1−i3−1+i32−1+i32−1−i31+i321−i32−1−i3−1+i32−1+i32−1−i300001−1−i32−1+i321+i31−i3-21−i3-21+i3000000000000000000000000
χ3233−3−3i32−3+3i32−3−3i32−3+3i320000-3-33+3i323+3i323−3i323−3i323−3−3i32−3+3i32000000-1-11+i321−i32−1+i32−1−i3−1−i3−1+i321+i321−i32−1+i32−1−i3−1−i3−1+i3200001−1−i32−1+i321−i3-21+i31+i31−i3-2000000000000000000000000
χ3333−3+3i32−3−3i32−3+3i32−3−3i32000033−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i3200000033−3+3i32−3−3i32000000−3+3i32−3−3i3200000000003−3+3i32−3−3i32000000000000000000000000000000
χ3433−3+3i32−3−3i32−3+3i32−3−3i32000033−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i32000000-1-11−i321+i322−1+i3−1−i32−1+i3−1−i31−i321+i322−1+i3−1−i32−1+i3−1−i30000-11−i321+i322−1+i3−1−i32−1+i3−1−i3000000000000000000000000
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χ3633−3+3i32−3−3i32−3+3i32−3−3i32000033−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i32000000-1-11−i321+i32−1+i3−1−i32−1−i32−1+i31−i321+i32−1+i3−1−i32−1−i32−1+i30000-11−i321+i32−1+i3−1−i32−1−i32−1+i3000000000000000000000000
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χ3833−3+3i32−3−3i32−3+3i32−3−3i320000-3-33−3i323−3i323+3i323+3i323−3+3i32−3−3i32000000-1-11−i321+i322−1+i3−1−i32−1+i3−1−i31−i321+i322−1+i3−1−i32−1+i3−1−i300001−1+i32−1−i32-21−i31+i3-21−i31+i3000000000000000000000000
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χ4033−3+3i32−3−3i32−3+3i32−3−3i320000-3-33−3i323−3i323+3i323+3i323−3+3i32−3−3i32000000-1-11−i321+i32−1+i3−1−i32−1−i32−1+i31−i321+i32−1+i3−1−i32−1−i32−1+i300001−1+i32−1−i321−i31+i3-21+i3-21−i3000000000000000000000000
χ414-444-4-444-4-42i−2i2i−2i2i−2i0000000000000000000000000002i−2i2i−2i000000000111111-1-1-1-1-1-1i−ii−ii−ii−ii−ii−i
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χ474-444-4-4−2−2i3−2+2i32+2i32−2i32i−2i2i−2i2i−2i0000000000000000000000000002ζ11−2ζ112ζ7−2ζ70000000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32i−iζ11−ζ11ζ7−ζ7i−iζ11−ζ11ζ7−ζ7
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χ7712-12−6−6i3−6+6i36+6i36−6i300006i−6i6ζ11−6ζ116ζ7−6ζ70000000000000000000000000000000000000000000000000000000000000000
χ7812-12−6−6i3−6+6i36+6i36−6i30000−6i6i−6ζ116ζ11−6ζ76ζ70000000000000000000000000000000000000000000000000000000000000000
χ7912-12−6+6i3−6−6i36−6i36+6i300006i−6i6ζ7−6ζ76ζ11−6ζ110000000000000000000000000000000000000000000000000000000000000000
χ8012-12−6+6i3−6−6i36−6i36+6i30000−6i6i−6ζ76ζ7−6ζ116ζ110000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.