Finite Group Databasebeta

← Group #10596623

Character table — Group #10596623

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222233444444466666668888888888121212121212121216161616161618181818242424242424
order12344464433661212122222224336612121212121266612121212121212121212122444666666
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−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+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+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−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ41111111-1-11111111111-1-1-1111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ51111111-1-1−1−i32−1+i32−1−i32−1+i32111111-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111+i321+i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321−i321−i321−i32
χ61111111-1-1−1+i32−1−i32−1+i32−1−i32111111-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−i321−i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321+i321+i321+i32
χ71111-1-111111111-1-11-1-11-1-1111111-1-11-1-11-1-1111111-1-11-1-111-1-11-1-11-1-1
χ81111-1-1111−1−i32−1+i32−1−i32−1+i321-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321-1-11−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i321+i321+i32−1+i321−i321−i32
χ91111-1-1111−1+i32−1−i32−1+i32−1−i321-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321-1-11−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i321−i321−i32−1−i321+i321+i32
χ101111-1-11-1-111111-1-11-1-1-111111111-1-11-1-11-1-11-1-1-1-11-1-11-1-1-1-111-111-111
χ111111-1-11-1-1−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1111−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321-1-111+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32-1-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ121111-1-11-1-1−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1111−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321-1-111−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32-1-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ13111-11-11111111-11-1-11-1-11-111111-11-1-11-1-11-111111-11-1-11-11-11-1-11-1-11-1
χ14111-11-1111−1−i32−1+i32−1−i32−1+i32-11-1-11-1-11-11−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32-11-11−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i321-11-11+i32−1−i321+i321−i32−1+i321−i32
χ15111-11-1111−1+i32−1−i32−1+i32−1−i32-11-1-11-1-11-11−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32-11-11−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i321-11-11−i32−1+i321−i321+i32−1−i321+i32
χ16111-11-11-1-11111-11-1-11-11-1111111-11-1-11-1-11-11-1-1-1-1-11-1-11-1-11-111-111-11
χ17111-11-11-1-1−1−i32−1+i32−1−i32−1+i32-11-1-11-11-111−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32-11-111+i321+i321−i321−i321+i32−1−i321+i321−i32−1+i321−i32-11-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ18111-11-11-1-1−1+i32−1−i32−1+i32−1−i32-11-1-11-11-111−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32-11-111−i321−i321+i321+i321−i32−1+i321−i321+i32−1−i321+i32-11-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ19111-1-111111111-1-11-1-11-1-1111111-1-11-1-11-1-1111111-1-11-1-111-1-11-1-11-1-11
χ20111-1-11111−1−i32−1+i32−1−i32−1+i32-1-11-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-111+i321+i32−1−i321−i321−i32−1+i32
χ21111-1-11111−1+i32−1−i32−1+i32−1−i32-1-11-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-111−i321−i32−1+i321+i321+i32−1−i32
χ22111-1-111-1-11111-1-11-1-1111-111111-1-11-1-11-1-111-1-1-1-1-1-11-1-11-111-111-111-1
χ23111-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-11-1-1111-11−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-1111+i321+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i32-111-1−1−i32−1−i321+i32−1+i32−1+i321−i32
χ24111-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-11-1-1111-11−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-1111−i321−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i32-111-1−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522-1222-1002222-1-1-12220002-1-1-1-1222222-1-1-1-10000-1-1-1-1-1-10000000000
χ2622-1222-100−1−i3−1+i3−1−i3−1+i3-1-1-122200021+i321−i321+i321−i32−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-1-100001+i321+i321+i321−i321−i321−i320000000000
χ2722-1222-100−1+i3−1−i3−1+i3−1−i3-1-1-122200021−i321+i321−i321+i32−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-1-100001−i321−i321−i321+i321+i321+i320000000000
χ2822-12-2-2-1002222-1112-2-20002-1-1-1-12-2-22-2-2-111-10000-111-1110000000000
χ2922-12-2-2-100−1−i3−1+i3−1−i3−1+i3-1112-2-200021+i321−i321+i321−i32−1−i31+i31+i3−1+i31−i31−i3-111-100001+i32−1−i32−1−i321−i32−1+i32−1+i320000000000
χ3022-12-2-2-100−1+i3−1−i3−1+i3−1−i3-1112-2-200021−i321+i321−i321+i32−1+i31−i31−i3−1−i31+i31+i3-111-100001−i32−1+i32−1+i321+i32−1−i32−1−i320000000000
χ3122-1-22-2-10022221-11-22-20002-1-1-1-1-22-2-22-21-11-100001-111-110000000000
χ3222-1-22-2-100−1−i3−1+i3−1−i3−1+i31-11-22-200021+i321−i321+i321−i321+i3−1−i31+i31−i3−1+i31−i31-11-10000−1−i321+i32−1−i32−1+i321−i32−1+i320000000000
χ3322-1-22-2-100−1+i3−1−i3−1+i3−1−i31-11-22-200021−i321+i321−i321+i321−i3−1+i31−i31+i3−1−i31+i31-11-10000−1+i321−i32−1+i32−1−i321+i32−1−i320000000000
χ3422-1-2-22-100222211-1-2-220002-1-1-1-1-2-22-2-2211-1-1000011-111-10000000000
χ3522-1-2-22-100−1−i3−1+i3−1−i3−1+i311-1-2-2200021+i321−i321+i321−i321+i31+i3−1−i31−i31−i3−1+i311-1-10000−1−i32−1−i321+i32−1+i32−1+i321−i320000000000
χ3622-1-2-22-100−1+i3−1−i3−1+i3−1−i311-1-2-2200021−i321+i321−i321+i321−i31−i3−1+i31+i31+i3−1−i311-1-10000−1+i32−1+i321−i32−1−i32−1−i321+i320000000000
χ373333333330000333-1-1-1333-10000000000-1-1-1-10000000000-1-1-1-1000000
χ383333333-3-30000333-1-1-1-3-3-3-10000000000-1-1-1-100000000001111000000
χ393333-3-333300003-3-3-1113-3-3-10000000000-111-10000000000-1-111000000
χ403333-3-33-3-300003-3-3-111-333-10000000000-111-1000000000011-1-1000000
χ41333-33-33330000-33-31-11-33-3-100000000001-11-10000000000-11-11000000
χ42333-33-33-3-30000-33-31-113-33-100000000001-11-100000000001-11-1000000
χ43333-3-333330000-3-3311-1-3-33-1000000000011-1-10000000000-111-1000000
χ44333-3-333-3-30000-3-3311-133-3-1000000000011-1-100000000001-1-11000000
χ454-44000-44i−4i-2-2220000000000-2-22200000000002i−2i2i−2i0000000000000000
χ464-44000-44i−4i1+i31−i3−1−i3−1+i300000000001+i31−i3−1−i3−1+i300000000002ζ11−2ζ112ζ7−2ζ70000000000000000
χ474-44000-44i−4i1−i31+i3−1+i3−1−i300000000001−i31+i3−1+i3−1−i300000000002ζ7−2ζ72ζ11−2ζ110000000000000000
χ484-44000-4−4i4i-2-2220000000000-2-2220000000000−2i2i−2i2i0000000000000000
χ494-44000-4−4i4i1+i31−i3−1−i3−1+i300000000001+i31−i3−1−i3−1+i30000000000−2ζ112ζ11−2ζ72ζ70000000000000000
χ504-44000-4−4i4i1−i31+i3−1+i3−1−i300000000001−i31+i3−1+i3−1−i30000000000−2ζ72ζ7−2ζ112ζ110000000000000000
χ5166-3666-3000000-3-3-3-2-2-2000-20000000000111100000000000000000000
χ5266-36-6-6-3000000-333-222000-200000000001-1-1100000000000000000000
χ5366-3-66-6-30000003-332-22000-20000000000-11-1100000000000000000000
χ5466-3-6-66-300000033-322-2000-20000000000-1-11100000000000000000000
χ558-8-4000400-4-444000000000022-2-2000000000000000000000000000000
χ568-8-40004002+2i32−2i3−2−2i3−2+2i30000000000−1−i3−1+i31+i31−i3000000000000000000000000000000
χ578-8-40004002−2i32+2i3−2+2i3−2−2i30000000000−1+i3−1−i31−i31+i3000000000000000000000000000000

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