Finite Group Databasebeta

← Group #72271454

Character table — Group #72271454

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122222222224444444444444444444444888888888888888888888888888888161616161616161616161616161616161616161616161616161624242424242424243232323232323232323232323232323232323232323232324848484848484848484848489696969696969696
order12222222223666222222222222222266666622444466666666666666666666121212124444444412121212121212121212121212121212121222222222444444441212121212121212121212121212121222444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1
χ91-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−i
χ101-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-11-1111-1-1-1-111ii−i−i−i−iii
χ111-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111-1-111−i−iii−i−iii
χ121-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-11-1-1-11111-1-1−i−iiiii−i−i
χ131-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii
χ141-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-11-1111-1-1-1-111−i−iiiii−i−i
χ151-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111-1-111ii−i−iii−i−i
χ161-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-11-1-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222-2-222222222-2-2222222-2-2-2-2-2-22222-2-2-2-2222222-2-222-2-2-2-2-2-200000000-2-20000000000000000222222220000000000000000000000000000-2-2-2-2000000000000
χ18222222222222222222-2-222222222-2-2222222-2-2-2-2-2-22222-2-2-2-2222222-2-222-2-2-2-2-2-200000000-2-20000000000000000-2-2-2-2-2-2-2-200000000000000000000000000002222000000000000
χ192222222222222222-2-22222-2-2-2-2-2-22222222222-2-2-2-222-2-2222222-2-2-2-222-2-222-2-2-2-200000000-2-200000000000000000000000000000000000000000000000000000000000000002-22-2
χ202222222222222222-2-22222-2-2-2-2-2-22222222222-2-2-2-222-2-2222222-2-2-2-222-2-222-2-2-2-200000000-2-20000000000000000000000000000000000000000000000000000000000000000-22-22
χ212222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-2222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222000000002200000000000000000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-2222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000220000000000000000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222222222-2-22222-2-2-2-2-2-22222222222-2-22-22-2-2-22222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000
χ2422222222222222-2-22222-2-2-2-2-2-22222222222-2-22-22-2-2-22222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ2522222222222222-2-222-2-2-2-2-2-2-2-222-2-222222222-22-22-2-222-2-222-2-222-2-2-2-2-2-222-2-2-2-200000000220000000000000000000000000000000000000000000000000000000000002-22-20000
χ2622222222222222-2-222-2-2-2-2-2-2-2-222-2-222222222-22-22-2-222-2-222-2-222-2-2-2-2-2-222-2-2-2-20000000022000000000000000000000000000000000000000000000000000000000000-22-220000
χ2722222222222222-2-2-2-222-2-22222-2-222222222-2-2-22-22-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-2000000002200000000000000000000000000000000000000000000000022220000-2-2-2-200000000
χ2822222222222222-2-2-2-222-2-22222-2-222222222-2-2-22-22-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-20000000022000000000000000000000000000000000000000000000000-2-2-2-20000222200000000
χ2922222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222-22-2-2-2-2-2-2-222-2-2-2-222-2-22222222200000000-2-20000000000000000000000002-22-2000022-2-222-2-20000000000000000000000000000
χ3022222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222-22-2-2-2-2-2-2-222-2-2-2-222-2-22222222200000000-2-2000000000000000000000000-22-220000-2-222-2-2220000000000000000000000000000
χ312222222222-1-1-1-12222222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ322222222222-1-1-1-12222222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ332222222222-1-1-1-12222222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111111111111000000002222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ342222222222-1-1-1-12222222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111100000000-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ352222222222-1-1-1-122-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-22222-1-1111111-1-11111111111-1-1-1-100000000-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000002i−2i2i−2i3−33−33−33−3−i−iii−i−iii00000000000000000000
χ362222222222-1-1-1-122-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-22222-1-1111111-1-11111111111-1-1-1-100000000-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000−2i2i−2i2i−33−33−33−33ii−i−iii−i−i00000000000000000000
χ372222222222-1-1-1-122-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-22222-1-1111111-1-11111111111-1-1-1-100000000-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000002i−2i2i−2i−33−33−33−33−i−iii−i−iii00000000000000000000
χ382222222222-1-1-1-122-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-22222-1-1111111-1-11111111111-1-1-1-100000000-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000−2i2i−2i2i3−33−33−33−3ii−i−iii−i−i00000000000000000000
χ392222222222-1-1-1-1-2-22222-2-2-2-2-2-22222-1-1-1-1-1-1-2-22-22-211-1-1-1-11111-1-111-1-11111-1-1-1-12222-2-2-2-211-1-1-1-1-1-1-1-11111111100000000000000003−3−333−3−333−33−33−33−300000000000000000000
χ402222222222-1-1-1-1-2-22222-2-2-2-2-2-22222-1-1-1-1-1-1-2-22-22-211-1-1-1-11111-1-111-1-11111-1-1-1-12222-2-2-2-211-1-1-1-1-1-1-1-1111111110000000000000000−333−3−333−3−33−33−33−3300000000000000000000
χ412222222222-1-1-1-1-2-22222-2-2-2-2-2-22222-1-1-1-1-1-1-2-22-22-211-1-1-1-11111-1-111-1-11111-1-1-1-1-2-2-2-222221111111111-1-1-1-1-1-1-1-100000000000000003−3−333−3−33−33−33−33−3300000000000000000000
χ422222222222-1-1-1-1-2-22222-2-2-2-2-2-22222-1-1-1-1-1-1-2-22-22-211-1-1-1-11111-1-111-1-11111-1-1-1-1-2-2-2-222221111111111-1-1-1-1-1-1-1-10000000000000000−333−3−333−33−33−33−33−300000000000000000000
χ432222222222-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1222-22-2111111-1-11111-1-111-1-1-1-1-1-1-1-10000000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000002-22-20000-1-111-1-111−i3i3i3−i3−i3i3i3−i300000000000000000000
χ442222222222-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1222-22-2111111-1-11111-1-111-1-1-1-1-1-1-1-10000000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000-22-22000011-1-111-1-1i3−i3−i3i3i3−i3−i3i300000000000000000000
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χ462222222222-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1222-22-2111111-1-11111-1-111-1-1-1-1-1-1-1-10000000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000-22-22000011-1-111-1-1−i3i3i3−i3−i3i3i3−i300000000000000000000
χ472-2-222-2-2-22222-2-22222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-2-2-2222222-2-22200000000-2200000000000000002222-2-2-2-20000000000000000000000000000-2-222000000000000
χ482-2-222-2-2-22222-2-22222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-2-2-2222222-2-22200000000-220000000000000000-2-2-2-22222000000000000000000000000000022-2-2000000000000
χ492-2-222-2-2-22222-2-222-2-222-2-222-2-222-2-2222-2-2-22-2-2-22222-2-22222-2-22222-2-2-2-2-2-2-2-22200000000-2200000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ502-2-222-2-2-22222-2-222-2-222-2-222-2-222-2-2222-2-2-22-2-2-22222-2-22222-2-22222-2-2-2-2-2-2-2-22200000000-220000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ512-2-222-2-2-22222-2-222-2-2-2-2-2-222-2-22222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-2222222-2-22222-2-2000000002-200000000000000000000000000002-2-220000000022-2-2-2-22200000000000000000000
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χ532-2-222-2-2-22222-2-2-2-222222222-2-2-2-2-2-2222-2-2-2-222-2-22-2-22222-2-222-2-222-2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i-222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000000000
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χ552-2-222-2-2-22222-2-2-2-222-2-22222-2-2-2-222222-2-2-22-2-222-2-2-222-2-22222-2-22222-2-2-2-2-2-222000000002-20000000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ562-2-222-2-2-22222-2-2-2-222-2-22222-2-2-2-222222-2-2-22-2-222-2-2-222-2-22222-2-22222-2-2-2-2-2-222000000002-2000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ572-2-222-2-2-22222-2-2-2-2-2-22222-2-22222-2-2222-2-2-2-22-222-2-2-2-2-222-2-22222-2-2-2-22222-2-222000000002-20000000000000000000000000000000000000000000000002-22-20000-2-22200000000
χ582-2-222-2-2-22222-2-2-2-2-2-22222-2-22222-2-2222-2-2-2-22-222-2-2-2-2-222-2-22222-2-2-2-22222-2-222000000002-2000000000000000000000000000000000000000000000000-22-22000022-2-200000000
χ592-2-222-2-2-22222-2-2-2-2-2-2-2-222-2-2222222222-2-2-22-22-2-22-2-2-2-2-2-2222222-2-22222-2-222-2-200000000-220000000000000000000000002-2-22000022-2-2-2-2220000000000000000000000000000
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χ612-2-222-2-2-222-1-111222222-2-2-2-222-2-2-2-2-1-1-11112-222-2-2-1-1-1-1-1-1-1-111111111-1-111-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000022-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii00000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.