Finite Group Databasebeta

← Group #13155932

Character table — Group #13155932

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222222222244444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272216
order122333446666612123336666666661212121212121212121212366661212121212121244121212121212121212121212121212122666666668242424242424242422444466121212128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111-1-1-11-11-11-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11-11-1-11
χ511111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-11-1-1-11-11-11-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-11-11-11-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
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χ1322222-122222-12222-1-1-1-1-12-1-12222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2111111222-1-1-1-1-1-10-2000-20101000
χ1422222-122222-12222-1-1-1-1-12-1-12222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2111111-2-2-21111110200020-10-1000
χ152222-122222-122-1-1-1-12222-1-12-1-1-1-1222-1-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000002-1-122-1-1-1-1200020-10-10000
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χ172222-122222-122-1-1-1-12222-1-12-1-1-1-1222-1-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-2-2-2-2-2-21111111111110000000002-1-122-1-1-1-1-2000-201010000
χ182222-122222-122-1-1-1-12222-1-12-1-1-1-1222-1-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-2-2-2-2-2-2111111111111000000000-211-2-21111200020-10-10000
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χ3022-2222-22-2-2222-2-2222-2-2-2222-2-2-222-22-2-222-2-2-22-2-2-22-222-2-222000000000000000000000000000000000000-200020-2020000
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χ3522-22-12-22-2-2-12211-1-12-2-2-2-1-12111-12-2211-1-1-211-1111-1-22-111-1-100000033−3−333−3−333−3−300000000003−3003−33−32000-20-1010000
χ3622-22-12-22-2-2-12211-1-12-2-2-2-1-12111-12-2211-1-1-211-1111-1-22-111-1-100000033−3−333−3−333−3−30000000000−3300−33−33-20002010-10000
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χ3944444-2-4-4444-24-4-44-2-2-2-2-24-2-2444-42-4-4-4-4-4-4222-2-2-2-2-222222220000000000000000000000000000000000000000000000000
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χ5844-44-2-2-44-4-4-2-2422-21-2222-21-2222-2-2-4422-2-22-1-11-1-1-112-21-1-1110000000000000000000000000000−2323003−33−30000000000000
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χ814-40-2-2400−2i32i32-42−23231-2-20−2i32i3-1220i3−i300003−3−3i3i0−232310i3−i3-10003−3−3i3i2i−2i2ζ7−2ζ72ζ11−2ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ10−2ζ2−ζ10−ζ112ζ2+ζ10+ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ110000000000000000000000000000000
χ824-40-2-2400−2i32i32-42−23231-2-20−2i32i3-1220i3−i300003−3−3i3i0−232310i3−i3-10003−3−3i3i−2i2i−2ζ72ζ7−2ζ112ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ102ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ110000000000000000000000000000000
χ834-40-2-24002i3−2i32-4223−231-2-202i3−2i3-1220−i3i30000−33−3i3i023−2310−i3i3-1000−33−3i3i2i−2i2ζ11−2ζ112ζ7−2ζ7−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ11−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ10ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ100000000000000000000000000000000
χ844-40-2-24002i3−2i32-4223−231-2-202i3−2i3-1220−i3i30000−33−3i3i023−2310−i3i3-1000−33−3i3i−2i2i−2ζ112ζ11−2ζ72ζ7ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ10−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ100000000000000000000000000000000
χ854-40-2-24002i3−2i32-42−23231-2-202i3−2i3-1220−i3i300003−33i−3i0−232310−i3i3-10003−33i−3i2i−2i2ζ11−2ζ112ζ7−2ζ7ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−2ζ2−ζ10−ζ112ζ2+ζ10+ζ112ζ2+ζ10−ζ11−2ζ2−ζ10+ζ11ζ2−ζ7+2ζ10−ζ2+ζ7−2ζ10−ζ2−ζ7−2ζ10ζ2+ζ7+2ζ100000000000000000000000000000000
χ864-40-2-24002i3−2i32-42−23231-2-202i3−2i3-1220−i3i300003−33i−3i0−232310−i3i3-10003−33i−3i−2i2i−2ζ112ζ11−2ζ72ζ7−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ112ζ2+ζ10+ζ11−2ζ2−ζ10−ζ11−2ζ2−ζ10+ζ112ζ2+ζ10−ζ11−ζ2+ζ7−2ζ10ζ2−ζ7+2ζ10ζ2+ζ7+2ζ10−ζ2−ζ7−2ζ100000000000000000000000000000000
χ87888-4-4-488-4-4-4-4-4-4-4222-422222-422-4-4-4-42222-422-12-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-4-4-444222-422222-4224444-2-2-2-24-2-2-12-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-844-4-4-4-4-42224-2-22224-2-244-4422-2-2-422-1-211-12-2-2-1-1110000000000000000000000000000000000000000000000000
χ9088-8-4-4-4-8844-4-4-4442224-2-22224-2-2-4-44-4-2-2224-2-2-1-211-1-22211-1-10000000000000000000000000000000000000000000000000
χ918-8088-40000-84-8008-4-4000-84400000000000000-4000400000000000000000000000000000000000000000000000000000000
χ928-808-4-4000044-843−43-42-40004-24000000043−43000−23232000-2000−2323000000000000000000000000000000000000000000000000000
χ938-808-4-4000044-8−4343-42-40004-240000000−434300023−232000-200023−23000000000000000000000000000000000000000000000000000
χ948-80-48-400−4i34i3-84400-4-4202i3−2i344-20−4i34i300000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000
χ958-80-48-4004i3−4i3-84400-4-420−2i32i344-204i3−4i30000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000
χ968-80-4-4-400−4i34i344443−4322202i3−2i3-2-2-202i3−2i30000−23236i−6i0−2323-10−i3i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ978-80-4-4-400−4i34i3444−434322202i3−2i3-2-2-202i3−2i3000023−23−6i6i023−23-10−i3i31000−333i−3i0000000000000000000000000000000000000000000000000
χ988-80-4-4-4004i3−4i344443−432220−2i32i3-2-2-20−2i32i30000−2323−6i6i0−2323-10i3−i310003−33i−3i0000000000000000000000000000000000000000000000000
χ998-80-4-4-4004i3−4i3444−43432220−2i32i3-2-2-20−2i32i3000023−236i−6i023−23-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000

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