Finite Group Databasebeta

← Group #13143895

Character table — Group #13143895

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111122222222244444466666666888888121212121212121212121212181818181818242424242424242424242424242424242424242424242424363636363636363636727272727272
order12336624466121212128824242424333366664812122424666612121212121212128824242424121212121212121224242424242424242424242424242424246681212242426682424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-1-1-1-1-1111111111-111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1
χ6111111111111111-1-1-1-1-1-1111111111-111-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111
χ7111111111111111-1-1-1-1-1-111111111-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-1111
χ8111111111111111-1-1-1-1-1-111111111-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1111-1-1-1
χ92222222222222222222222-1-1-12-1-1-12222222-1-1-122-1-1-1-1-1-100000022-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000
χ102222222222222222222222-1-1-12-1-1-1-2-2-2-2-2-22-1-1-122-1-1-1-1-1-1000000-2-211111122-1-1-1-1-1-1-2-2111111000000000000000
χ11222222222222222222222-12-1-1-12-1-1222222-12-1-1-1-122-1-1-1-1000000-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000
χ12222222222222222222222-12-1-1-12-1-1-2-2-2-2-2-2-12-1-1-1-122-1-1-1-100000011-2-21111-1-122-1-1-1-111-2-21111000000000000000
χ13222222222222222222222-1-12-1-1-12-1222222-1-12-1-1-1-1-122-1-1000000-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000
χ14222222222222222222222-1-12-1-1-12-1-2-2-2-2-2-2-1-12-1-1-1-1-122-1-10000001111-2-211-1-1-1-122-1-11111-2-211000000000000000
χ15222222222222222222222-1-1-12-1-1-12222222-1-1-12-1-1-1-1-1-122000000-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000
χ16222222222222222222222-1-1-12-1-1-12-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122000000111111-2-2-1-1-1-1-1-122111111-2-2000000000000000
χ17222222222222222-2-2-2-2-2-22-1-1-12-1-1-12-222-2-22-1-1-122-1-1-1-1-1-100000022-1-1-1-1-1-1-2-2111111-2-2111111000000000000000
χ18222222222222222-2-2-2-2-2-22-1-1-12-1-1-1-22-2-2222-1-1-122-1-1-1-1-1-1000000-2-2111111-2-211111122-1-1-1-1-1-1000000000000000
χ19222222222222222-2-2-2-2-2-2-12-1-1-12-1-12-222-2-2-12-1-1-1-122-1-1-1-1000000-1-122-1-1-1-111-2-2111111-2-21111000000000000000
χ20222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-22-2-222-12-1-1-1-122-1-1-1-100000011-2-2111111-2-21111-1-122-1-1-1-1000000000000000
χ21222222222222222-2-2-2-2-2-2-1-12-1-1-12-12-222-2-2-1-12-1-1-1-1-122-1-1000000-1-1-1-122-1-11111-2-2111111-2-211000000000000000
χ22222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-22-2-222-1-12-1-1-1-1-122-1-10000001111-2-2111111-2-211-1-1-1-122-1-1000000000000000
χ23222222222222222-2-2-2-2-2-2-1-1-12-1-1-122-222-2-2-1-1-12-1-1-1-1-1-122000000-1-1-1-1-1-122111111-2-2111111-2-2000000000000000
χ24222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-22-2-222-1-1-12-1-1-1-1-1-122000000111111-2-2111111-2-2-1-1-1-1-1-122000000000000000
χ252222222-2-222-2-2-2-22i−2i2i2i−2i−2i222222220000002222-2-2-2-2-2-2-2-2000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000
χ262222222-2-222-2-2-2-22i−2i2i2i−2i−2i2-1-1-12-1-1-10000002-1-1-1-2-211111100000000−i3i3−i3i3−i3i32i−2i−ii−ii−ii003−33−33−3000000000000000
χ272222222-2-222-2-2-2-22i−2i2i2i−2i−2i2-1-1-12-1-1-10000002-1-1-1-2-211111100000000i3−i3i3−i3i3−i32i−2i−ii−ii−ii00−33−33−33000000000000000
χ282222222-2-222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-12-1-1000000-12-1-111-2-21111000000−i3i300−i3i3i3−i3−ii2i−2i−ii−ii3−3003−3−33000000000000000
χ292222222-2-222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-12-1-1000000-12-1-111-2-21111000000i3−i300i3−i3−i3i3−ii2i−2i−ii−ii−3300−333−3000000000000000
χ302222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-12-1-1-12-1000000-1-12-11111-2-211000000−i3i3i3−i300−i3i3−ii−ii2i−2i−ii3−3−33003−3000000000000000
χ312222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-12-1-1-12-1000000-1-12-11111-2-211000000i3−i3−i3i300i3−i3−ii−ii2i−2i−ii−333−300−33000000000000000
χ322222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-1-12-1-1-12000000-1-1-12111111-2-2000000−i3i3−i3i3i3−i300−ii−ii−ii2i−2i3−33−3−3300000000000000000
χ332222222-2-222-2-2-2-22i−2i2i2i−2i−2i-1-1-12-1-1-12000000-1-1-12111111-2-2000000i3−i3i3−i3−i3i300−ii−ii−ii2i−2i−33−333−300000000000000000
χ342222222-2-222-2-2-2-2−2i2i−2i−2i2i2i222222220000002222-2-2-2-2-2-2-2-200000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000
χ352222222-2-222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-12-1-1-10000002-1-1-1-2-211111100000000−i3i3−i3i3−i3i3−2i2ii−ii−ii−i00−33−33−33000000000000000
χ362222222-2-222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-12-1-1-10000002-1-1-1-2-211111100000000i3−i3i3−i3i3−i3−2i2ii−ii−ii−i003−33−33−3000000000000000
χ372222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-12-1-1000000-12-1-111-2-21111000000−i3i300−i3i3i3−i3i−i−2i2ii−ii−i−3300−333−3000000000000000
χ382222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-12-1-1000000-12-1-111-2-21111000000i3−i300i3−i3−i3i3i−i−2i2ii−ii−i3−3003−3−33000000000000000
χ392222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-12-1-1-12-1000000-1-12-11111-2-211000000−i3i3i3−i300−i3i3i−ii−i−2i2ii−i−333−300−33000000000000000
χ402222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-12-1-1-12-1000000-1-12-11111-2-211000000i3−i3−i3i300i3−i3i−ii−i−2i2ii−i3−3−33003−3000000000000000
χ412222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-1-12-1-1-12000000-1-1-12111111-2-2000000−i3i3−i3i3i3−i300i−ii−ii−i−2i2i−33−333−300000000000000000
χ422222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-1-1-12-1-1-12000000-1-1-12111111-2-2000000i3−i3i3−i3−i3i300i−ii−ii−i−2i2i3−33−3−3300000000000000000
χ43222222-22-2-2-222-2-200000022222222000000-2-2-2-22-22-22-22-22222220000000000000000000000000000-200-2-2000000
χ44222222-22-2-2-222-2-200000022222222000000-2-2-2-22-22-22-22-2-2-2-2-2-2-2000000000000000000000000000020022000000
χ45222222-2-22-2-2-2-22200000022222222000000-2-2-2-2-22-22-22-220000000000000000000000000000002-2220-2-200000000
χ46222222-2-22-2-2-2-22200000022222222000000-2-2-2-2-22-22-22-22000000000000000000000000000000-22-2-202200000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000033−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1−i32−1+i32−1+i3200000000000000000000000011−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000033−3−3i32−3+3i32−3−3i32−3+3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1-11+i321−i32-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1−i32−1+i32−1+i3200000000000000000000000011−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-3-33+3i323−3i323+3i323−3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1-11+i321−i32-11+i321−i321+i321−i321−1−i32−1+i321−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000003-3−3−3i32−3+3i323+3i323−3i3200000000000011−1−i32−1−i32−1+i32−1+i32000000000000000000000000-1-11+i321−i3211+i321−i32−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000003-3−3−3i32−3+3i323+3i323−3i32000000000000-1-11+i321+i321−i321−i3200000000000000000000000011−1−i32−1+i32-1−1−i32−1+i321+i321−i32-11+i321−i321−1−i32−1+i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000-333+3i323−3i32−3−3i32−3+3i3200000000000011−1−i32−1−i32−1+i32−1+i32000000000000000000000000-1-11+i321−i3211+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000-333+3i323−3i32−3−3i32−3+3i32000000000000-1-11+i321+i321−i321−i3200000000000000000000000011−1−i32−1+i32-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1+i32−1−i32−1−i3200000000000000000000000011−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1-11−i321+i32-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1+i32−1−i32−1−i3200000000000000000000000011−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i32
χ5833−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-3-33−3i323+3i323−3i323+3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1-11−i321+i32-11−i321+i321−i321+i321−1+i32−1−i321−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000003-3−3+3i32−3−3i323−3i323+3i3200000000000011−1+i32−1+i32−1−i32−1−i32000000000000000000000000-1-11−i321+i3211−i321+i32−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000003-3−3+3i32−3−3i323−3i323+3i32000000000000-1-11−i321−i321+i321+i3200000000000000000000000011−1+i32−1−i32-1−1+i32−1−i321−i321+i32-11−i321+i321−1+i32−1−i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000-333−3i323+3i32−3+3i32−3−3i3200000000000011−1+i32−1+i32−1−i32−1−i32000000000000000000000000-1-11−i321+i3211−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000-333−3i323+3i32−3+3i32−3−3i32000000000000-1-11−i321−i321+i321+i3200000000000000000000000011−1+i32−1−i32-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32
χ63444444-44-4-4-444-4-40000004-2-2-24-2-2-2000000-42224-4-22-22-22000000000000000000000000000000000000000000000
χ64444444-44-4-4-444-4-4000000-24-2-2-24-2-20000002-422-224-4-22-22000000000000000000000000000000000000000000000
χ65444444-44-4-4-444-4-4000000-2-24-2-2-24-200000022-42-22-224-4-22000000000000000000000000000000000000000000000
χ66444444-44-4-4-444-4-4000000-2-2-24-2-2-24000000222-4-22-22-224-4000000000000000000000000000000000000000000000
χ67444444-4-44-4-4-4-4440000004-2-2-24-2-2-2000000-4222-442-22-22-2000000000000000000000000000000000000000000000
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χ70444444-4-44-4-4-4-444000000-2-2-24-2-2-24000000222-42-22-22-2-44000000000000000000000000000000000000000000000
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χ7366−3−3i3−3+3i3−3−3i3−3+3i36-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i36i−6i6ζ226ζ14−6ζ22−6ζ1400000000000000000000000000000000000000000000000000000000000000000000000
χ7466−3−3i3−3+3i3−3−3i3−3+3i36-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i3−6i6i−6ζ22−6ζ146ζ226ζ1400000000000000000000000000000000000000000000000000000000000000000000000
χ7566−3−3i3−3+3i3−3−3i3−3+3i3-66-63+3i33−3i3−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000022−1−i3−1−i3−1+i3−1+i30000000000000000000000000000-2001+i31−i3000000
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χ7766−3−3i3−3+3i3−3−3i3−3+3i3-6-663+3i33−3i33+3i33−3i3−3−3i3−3+3i3000000000000000000000000000000000000000000000000000000000000002-2−1−i3−1+i301+i31−i300000000
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χ7966−3+3i3−3−3i3−3+3i3−3−3i36-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i36i−6i6ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000000000000000000000
χ8066−3+3i3−3−3i3−3+3i3−3−3i36-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i3−6i6i−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000000000000000000000
χ8166−3+3i3−3−3i3−3+3i3−3−3i3-66-63−3i33+3i3−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000022−1+i3−1+i3−1−i3−1−i30000000000000000000000000000-2001−i31+i3000000
χ8266−3+3i3−3−3i3−3+3i3−3−3i3-66-63−3i33+3i3−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000-2-21−i31−i31+i31+i30000000000000000000000000000200−1+i3−1−i3000000
χ8366−3+3i3−3−3i3−3+3i3−3−3i3-6-663−3i33+3i33−3i33+3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000000000000002-2−1+i3−1−i301−i31+i300000000
χ8466−3+3i3−3−3i3−3+3i3−3−3i3-6-663−3i33+3i33−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000-221−i31+i30−1+i3−1−i300000000
χ858-888-8-80000000000000008-4-4-4-8444000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-8000000000000000-48-4-44-844000000000000000000000000000000000000000000000000000000000000000
χ878-888-8-8000000000000000-4-48-444-84000000000000000000000000000000000000000000000000000000000000000
χ888-888-8-8000000000000000-4-4-48444-8000000000000000000000000000000000000000000000000000000000000000
χ8912-12−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000−2i22i22ζ7+2ζ13−2ζ7−2ζ132ζ5+2ζ23−2ζ5−2ζ23000000000000000000000000000000000000000
χ9012-12−6−6i3−6+6i36+6i36−6i3000000000000000000000000000000000000000002i2−2i2−2ζ7−2ζ132ζ7+2ζ13−2ζ5−2ζ232ζ5+2ζ23000000000000000000000000000000000000000
χ9112-12−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000−2i22i22ζ5+2ζ23−2ζ5−2ζ232ζ7+2ζ13−2ζ7−2ζ13000000000000000000000000000000000000000
χ9212-12−6+6i3−6−6i36−6i36+6i3000000000000000000000000000000000000000002i2−2i2−2ζ5−2ζ232ζ5+2ζ23−2ζ7−2ζ132ζ7+2ζ13000000000000000000000000000000000000000

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