Finite Group Databasebeta

← Group #72220461

Character table — Group #72220461

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112223344666666666661212121212121212121212121212161616161616161632323232323248484848646464646464646464646464
order12222224422222222222222244444444442334446666666644446612121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ41111111111111111111111111111111111-111-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ51111111111111111111111111111111111-1−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ61111111111111111111111111111111111-1−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ71111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-11111-1-1-1-1-1-1-1-1
χ81111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-11−1−i32−1+i321-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ91111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-11−1+i32−1−i321-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ101111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-111-1-1-1-1-1-111-1-111
χ111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ121111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ13111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i111-1i−i1111-1-1-1-11-1i−i11-1-1i−ii−ii−ii−i
χ14111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i1−1−i32−1+i32-1i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ15111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i1−1+i32−1−i32-1i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ16111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i-1111−ii1111-1-1-1-1-11−ii-1-111i−i−iii−i−ii
χ17111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i-1−1−i32−1+i321−ii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11−ii1+i321−i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ18111-1-111i−i11111-1-1-1-1-1-111-1-1iiiii−i−i−i−i−i-1−1+i32−1−i321−ii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11−ii1−i321+i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ19111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii111-1−ii1111-1-1-1-11-1−ii11-1-1−ii−ii−ii−ii
χ20111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii1−1−i32−1+i32-1−ii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ21111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii1−1+i32−1−i32-1−ii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ22111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii-1111i−i1111-1-1-1-1-11i−i-1-111−iii−i−iii−i
χ23111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii-1−1−i32−1+i321i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11i−i1+i321−i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ24111-1-111−ii11111-1-1-1-1-1-111-1-1−i−i−i−i−iiiiii-1−1+i32−1−i321i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11i−i1−i321+i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ2522-22-222002222-2-2-2-2-2-22-2-222000000000002200022-2-22-22-20000000000000000
χ2622-22-222002222-2-2-2-2-2-22-2-22200000000000−1−i3−1+i3000−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000000000000000
χ2722-22-222002222-2-2-2-2-2-22-2-22200000000000−1+i3−1−i3000−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000000000000000
χ2822-2-2222002222-222222-2-2-2-2-2000000000002200022-2-2-22-220000000000000000
χ2922-2-2222002222-222222-2-2-2-2-200000000000−1−i3−1+i3000−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i30000000000000000
χ3022-2-2222002222-222222-2-2-2-2-200000000000−1+i3−1−i3000−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i30000000000000000
χ31333333333-1-1-1-133-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-130033300000000-1-1-1-1000000000000
χ32333333333-1-1-1-133-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-1-300-3-3-3000000001111000000000000
χ333333333-3-3-1-1-1-133-1-1-1-13-1-1-1-1-31111-311113003-3-300000000-1-111000000000000
χ343333333-3-3-1-1-1-133-1-1-1-13-1-1-1-1-31111-31111-300-3330000000011-1-1000000000000
χ35333-3-3333i−3i-1-1-1-13-31111-3-1-1113i−i−i−i−i−3iiiii300-33i−3i00000000-11−ii000000000000
χ36333-3-3333i−3i-1-1-1-13-31111-3-1-1113i−i−i−i−i−3iiiii-3003−3i3i000000001-1i−i000000000000
χ37333-3-333−3i3i-1-1-1-13-31111-3-1-111−3iiiii3i−i−i−i−i300-3−3i3i00000000-11i−i000000000000
χ38333-3-333−3i3i-1-1-1-13-31111-3-1-111−3iiiii3i−i−i−i−i-30033i−3i000000001-1−ii000000000000
χ394-40004-40044-4-4000000000000000000000044000-4-40000000000000000000000
χ404-40004-40044-4-40000000000000000000000−2−2i3−2+2i30002+2i32−2i30000000000000000000000
χ414-40004-40044-4-40000000000000000000000−2+2i3−2−2i30002−2i32+2i30000000000000000000000
χ4266666-2-2662-22-2-2-222-2-2-22-22-2-222-2-2-222-2-2000000000000000000000000000000
χ4366666-2-266-22-22-2-2-2-222-2-22-22-2-2-222-2-2-222000000000000000000000000000000
χ4466666-2-2-6-62-22-2-2-222-2-2-22-22-22-2-2222-2-222000000000000000000000000000000
χ4566666-2-2-6-6-22-22-2-2-2-222-2-22-22222-2-2222-2-2000000000000000000000000000000
χ46666-6-6-2-26i−6i2-22-2-22-2-22222-2-22−2i2i2i−2i−2i2i−2i−2i2i2i000000000000000000000000000000
χ47666-6-6-2-26i−6i-22-22-2222-2-22-222-2−2i−2i−2i2i2i2i2i2i−2i−2i000000000000000000000000000000
χ48666-6-6-2-2−6i6i2-22-2-22-2-22222-2-222i−2i−2i2i2i−2i2i2i−2i−2i000000000000000000000000000000
χ49666-6-6-2-2−6i6i-22-22-2222-2-22-222-22i2i2i−2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ5066-66-66600-2-2-2-2-6-62222622-2-20000000000000000000000000000000000000000
χ5166-66-6-2-2002-22-222-2-222-2-222-204i−4i0004i−4i00000000000000000000000000000000
χ5266-66-6-2-2002-22-222-2-222-2-222-20−4i4i000−4i4i00000000000000000000000000000000
χ5366-66-6-2-200-22-222222-2-2-22-2-220004i−4i0004i−4i000000000000000000000000000000
χ5466-66-6-2-200-22-222222-2-2-22-2-22000−4i4i000−4i4i000000000000000000000000000000
χ5566-6-666600-2-2-2-2-66-2-2-2-2-622220000000000000000000000000000000000000000
χ5666-6-66-2-2002-22-22-222-2-22-22-2204-4000-4400000000000000000000000000000000
χ5766-6-66-2-2002-22-22-222-2-22-22-220-440004-400000000000000000000000000000000
χ5866-6-66-2-200-22-222-2-2-22222-22-20004-4000-44000000000000000000000000000000
χ5966-6-66-2-200-22-222-2-2-22222-22-2000-440004-4000000000000000000000000000000
χ6012-1200012-1200-4-444000000000000000000000000000000000000000000000000000
χ6112-12000-44004-4-44008-800000000000000000000000000000000000000000000000
χ6212-12000-44004-4-4400-8800000000000000000000000000000000000000000000000
χ6312-12000-4400-444-400008-8000000000000000000000000000000000000000000000
χ6412-12000-4400-444-40000-88000000000000000000000000000000000000000000000

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