Finite Group Databasebeta

← Group #11921150

Character table — Group #11921150

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1133446666121216161616161616162266881212121224243232323232323232339912121818181836364848484848484848
order12224444444433661212121236661212121212121212336612121212222244444444666612121212
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111-1-11111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ51111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ61111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ71-11-1i−i11-1-1i−i11-1-1i−ii−i1-11-1i−i11-1-1i−i11-1-1i−ii−i1-11-1i−i11-1-1i−i11-1-1i−ii−i
χ81-11-1i−i11-1-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ71-11-1i−i11-1-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ71-11-1i−i11-1-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7
χ91-11-1i−i11-1-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ111-11-1i−i11-1-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ111-11-1i−i11-1-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11
χ101-11-1−ii11-1-1−ii11-1-1−ii−ii1-11-1−ii11-1-1−ii11-1-1−ii−ii1-11-1−ii11-1-1−ii11-1-1−ii−ii
χ111-11-1−ii11-1-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ71-11-1−ii11-1-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ71-11-1−ii11-1-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7
χ121-11-1−ii11-1-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ111-11-1−ii11-1-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ111-11-1−ii11-1-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11
χ13333333-1-1-1-1-1-100000000333333-1-1-1-1-1-100000000333333-1-1-1-1-1-100000000
χ143333-3-3-1-1-1-111000000003333-3-3-1-1-1-111000000003333-3-3-1-1-1-11100000000
χ153-33-33i−3i-1-111−ii000000003-33-33i−3i-1-111−ii000000003-33-33i−3i-1-111−ii00000000
χ163-33-3−3i3i-1-111i−i000000003-33-3−3i3i-1-111i−i000000003-33-3−3i3i-1-111i−i00000000
χ1766-2-2002i−2i2i−2i000000000066-2-2002i−2i2i−2i000000000066-2-2002i−2i2i−2i0000000000
χ1866-2-200−2i2i−2i2i000000000066-2-200−2i2i−2i2i000000000066-2-200−2i2i−2i2i0000000000
χ196-6-22002i−2i−2i2i00000000006-6-22002i−2i−2i2i00000000006-6-22002i−2i−2i2i0000000000
χ206-6-2200−2i2i2i−2i00000000006-6-2200−2i2i2i−2i00000000006-6-2200−2i2i2i−2i0000000000
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ22111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ23111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ241111-1-11111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ251111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-11111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-111-1-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ261111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-11111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-111-1-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ271-11-1i−i11-1-1i−i11-1-1i−ii−i1-11-1i−i11-1-1i−i11-1-1i−ii−i-11-11−ii-1-111−ii-1-111−ii−ii
χ281-11-1i−i11-1-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ71-11-1i−i11-1-1i−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7-11-11−ii-1-111−ii1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7
χ291-11-1i−i11-1-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ111-11-1i−i11-1-1i−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11-11-11−ii-1-111−ii1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11
χ301-11-1−ii11-1-1−ii11-1-1−ii−ii1-11-1−ii11-1-1−ii11-1-1−ii−ii-11-11i−i-1-111i−i-1-111i−ii−i
χ311-11-1−ii11-1-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ71-11-1−ii11-1-1−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7-11-11i−i-1-111i−i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7
χ321-11-1−ii11-1-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ111-11-1−ii11-1-1−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11-11-11i−i-1-111i−i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11
χ33333333-1-1-1-1-1-100000000333333-1-1-1-1-1-100000000-3-3-3-3-3-311111100000000
χ343333-3-3-1-1-1-111000000003333-3-3-1-1-1-11100000000-3-3-3-3331111-1-100000000
χ353-33-33i−3i-1-111−ii000000003-33-33i−3i-1-111−ii00000000-33-33−3i3i11-1-1i−i00000000
χ363-33-3−3i3i-1-111i−i000000003-33-3−3i3i-1-111i−i00000000-33-333i−3i11-1-1−ii00000000
χ3766-2-2002i−2i2i−2i000000000066-2-2002i−2i2i−2i0000000000-6-62200−2i2i−2i2i0000000000
χ3866-2-200−2i2i−2i2i000000000066-2-200−2i2i−2i2i0000000000-6-622002i−2i2i−2i0000000000
χ396-6-22002i−2i−2i2i00000000006-6-22002i−2i−2i2i0000000000-662-200−2i2i2i−2i0000000000
χ406-6-2200−2i2i2i−2i00000000006-6-2200−2i2i2i−2i0000000000-662-2002i−2i−2i2i0000000000
χ4122222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ42222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i3200000000000000000000
χ43222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i3200000000000000000000
χ442222-2-22222-2-22222-2-2-2-2-1-1-1-111-1-1-1-111-1-1-1-1111100000000000000000000
χ452222-2-22222-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-1-1-1-111-1-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ462222-2-22222-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-1-1-1-111-1-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ472-22-22i−2i22-2-22i−2i22-2-22i−2i2i−2i-11-11−ii-1-111−ii-1-111−ii−ii00000000000000000000
χ482-22-22i−2i22-2-22i−2i−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ7-11-11−ii-1-111−ii1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700000000000000000000
χ492-22-22i−2i22-2-22i−2i−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ11-11-11−ii-1-111−ii1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100000000000000000000
χ502-22-2−2i2i22-2-2−2i2i22-2-2−2i2i−2i2i-11-11i−i-1-111i−i-1-111i−ii−i00000000000000000000
χ512-22-2−2i2i22-2-2−2i2i−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ7-11-11i−i-1-111i−i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700000000000000000000
χ522-22-2−2i2i22-2-2−2i2i−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ11-11-11i−i-1-111i−i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100000000000000000000
χ53666666-2-2-2-2-2-200000000-3-3-3-3-3-31111110000000000000000000000000000
χ546666-6-6-2-2-2-22200000000-3-3-3-3331111-1-10000000000000000000000000000
χ556-66-66i−6i-2-222−2i2i00000000-33-33−3i3i11-1-1i−i0000000000000000000000000000
χ566-66-6−6i6i-2-2222i−2i00000000-33-333i−3i11-1-1−ii0000000000000000000000000000
χ571212-4-4004i−4i4i−4i0000000000-6-62200−2i2i−2i2i000000000000000000000000000000
χ581212-4-400−4i4i−4i4i0000000000-6-622002i−2i2i−2i000000000000000000000000000000
χ5912-12-44004i−4i−4i4i0000000000-662-200−2i2i2i−2i000000000000000000000000000000
χ6012-12-4400−4i4i4i−4i0000000000-662-2002i−2i−2i2i000000000000000000000000000000

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