Finite Group Databasebeta

← Group #13161750

Character table — Group #13161750

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11112222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444499991818181818181818181818181818181818181818181836363636363636367272727272727272
order122233344666666666888812121212242424242424242433333666666666666666121212121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424444422666688881212121224242424242424242244444466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-111
χ91-1-111111-1-1-1-1-111-1-11ii−i−i11-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i1-1i−ii−i1-11-1i−ii−i1-1
χ101-1-111111-1-1-1-1-111-1-11ii−i−i11-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii−ii-11-11−ii−ii-11
χ111-1-111111-1-1-1-1-111-1-11ii−i−i11-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-11-1-111−i−iii-1-111−i−i−i−iiiii1-1i−i−ii-111-1i−i−ii-11
χ121-1-111111-1-1-1-1-111-1-11ii−i−i11-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-11-1-111−i−iii-1-111−i−i−i−iiiii-11−iii−i1-1-11−iii−i1-1
χ131-1-111111-1-1-1-1-111-1-11−i−iii11-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii11-1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii1-1−ii−ii1-11-1−ii−ii1-1
χ141-1-111111-1-1-1-1-111-1-11−i−iii11-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii11-1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii-11i−ii−i-11-11i−ii−i-11
χ151-1-111111-1-1-1-1-111-1-11−i−iii11-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii-1-111-11-1-111ii−i−i-1-111iiii−i−i−i−i1-1−iii−i-111-1−iii−i-11
χ161-1-111111-1-1-1-1-111-1-11−i−iii11-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii-1-111-11-1-111ii−i−i-1-111iiii−i−i−i−i-11i−i−ii1-1-11i−i−ii1-1
χ172222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-2-2-2-2-2-200002222000000000000000000000000
χ182222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-22222220000-2-2-2-2000000000000000000000000
χ19222222-122222-1-122-1222222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000022220000-1-1-1-10000
χ20222222-122222-1-122-1222222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-2-2-2000011110000
χ21222222-122222-1-122-12-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000022-2-20000-1-1110000
χ22222222-122222-1-122-12-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111111111100000000000000000000000000-2-222000011-1-10000
χ2322222-12222-1-122-12222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2422222-12222-1-122-12222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-21111111111110000000000000000
χ2522222-12222-1-122-1222-2-2-2-2-1-1-1-111111111-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-21111-2-2-2-2-2-2111111111111-2-21111-2-2-2-2-2-2111111111111222222-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2622222-12222-1-122-1222-2-2-2-2-1-1-1-111111111-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-21111-2-2-2-2-2-2111111111111-2-21111-2-2-2-2-2-2111111111111-2-2-2-2-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ2722222-12-2-22-1-122-12220000111133−3−333−3−3-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-211-2-21111110033−3−3000000333333−3−3−3−3−3−30033−3−3000000333333−3−3−3−3−3−32222-2-211110000-1-1-1-133−3−333−3−30000000000000000
χ2822222-12-2-22-1-122-12220000111133−3−333−3−3-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-211-2-21111110033−3−3000000333333−3−3−3−3−3−30033−3−3000000333333−3−3−3−3−3−3-2-2-2-222-1-1-1-100001111−3−333−3−3330000000000000000
χ2922222-12-2-22-1-122-122200001111−3−333−3−333-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-211-2-211111100−3−333000000−3−3−3−3−3−333333300−3−333000000−3−3−3−3−3−33333332222-2-211110000-1-1-1-1−3−333−3−3330000000000000000
χ3022222-12-2-22-1-122-122200001111−3−333−3−333-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-211-2-211111100−3−333000000−3−3−3−3−3−333333300−3−333000000−3−3−3−3−3−3333333-2-2-2-222-1-1-1-10000111133−3−333−3−30000000000000000
χ312222-12222-122222-12-12222222222222222-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-100000000000000000000000000000022220000-1-1-1-1
χ322222-12222-122222-12-12222222222222222-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000000000-2-2-2-200001111
χ332222-12222-122222-12-1-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1111111-2-21111-2-21111-2-21111111111-2-21111-2-21111-2-2111100000000000000000000000000000022-2-20000-1-111
χ342222-12222-122222-12-1-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1111111-2-21111-2-21111-2-21111111111-2-21111-2-21111-2-21111000000000000000000000000000000-2-222000011-1-1
χ3522-2-22220022-2-2-2-2-22-22−22−200002−22−22−22−2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000002−22−22−22−222−2−22−222−2−22−222−2−22−22−22−22−222−2−22−222−2−22−222−2−22i−2i2i−2i000000−i2i2−i2i22i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3622-2-22220022-2-2-2-2-22-22−22−200002−22−22−22−2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000002−22−22−22−222−2−22−222−2−22−222−2−22−22−22−22−222−2−22−222−2−22−222−2−2−2i2i−2i2i000000i2−i2i2−i2−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3722-2-22220022-2-2-2-2-22-2−22−220000−22−22−22−22222222-22-22-222-2-2-2-2-2-2-2000000000000000000000000−22−22−22−22−2−222−22−2−222−22−2−222−22−22−22−22−2−222−22−2−222−22−2−2222i−2i2i−2i000000i2−i2i2−i22i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-2-22220022-2-2-2-2-22-2−22−220000−22−22−22−22222222-22-22-222-2-2-2-2-2-2-2000000000000000000000000−22−22−22−22−2−222−22−2−222−22−2−222−22−22−22−22−2−222−22−2−222−22−2−222−2i2i−2i2i000000−i2i2−i2i2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-2-22-12002-11-2-21-22-22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-12-1-1-1-112-2-11-1-1111-2111003−3003−333−3−3003−3003−333−3−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−222−2−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−222−2−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232i−2i2i−2i00−i3i3−i3i3−i2i2−i2i2−ii−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4022-2-22-12002-11-2-21-22-22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-12-1-1-1-112-2-11-1-1111-2111003−3003−333−3−3003−3003−333−3−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−222−2−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−222−2−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−2i2i−2i2i00i3−i3i3−i3i2−i2i2−i2i−ii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
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χ1674-4-44-2-2-2-442222-2-222-2000022-2-22i32i3−2i3−2i3−2i3−2i32i32i3111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i3200−i3−i3i3i300-33-33−i3−i33+i32−3+i323+i32−3+i32i3i33−i32−3−i323−i32−3−i3200i3i3−i3−i3003-33-3i3i3−3−i323−i32−3−i323−i32−i3−i3−3+i323+i32−3+i323+i32000000000000000000000000000000000000000000
χ1684-4-44-2-2-2-442222-2-222-2000022-2-22i32i3−2i3−2i3−2i3−2i32i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i3200−i3−i3i3i3003-33-3−i3−i3−3+i323+i32−3+i323+i32i3i3−3−i323−i32−3−i323−i3200i3i3−i3−i300-33-33i3i33−i32−3−i323−i32−3−i32−i3−i33+i32−3+i323+i32−3+i32000000000000000000000000000000000000000000

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