Finite Group Databasebeta

← Group #11921151

Character table — Group #11921151

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1122333344666666889912121212121212121616161616161616181818182424323232323232323236364848484848484848
order12362244444444661212442244121212123366121212124444121233661212121244666612121212
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ31111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411111111-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1111111-1-111-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ611111111-1-1111111-1-111-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ7111111-1-11111111111-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ8111111-1-11111111111-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ9111111-1-11111111111-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ10111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ11111111-1-1-1-1111111-1-1-1-111-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ12111111-1-1-1-1111111-1-1-1-111-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ131-11-11-1i−ii−i11-1-11-1i−ii−i1-1i−i11-1-111-1-1i−ii−iii−i−ii−i11-1-1i−ii−i1-11-11-1i−ii−i
χ141-11-11-1i−ii−i11-1-11-1i−ii−i1-1i−i11-1-1−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7ii−i−ii−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ71-1−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7
χ151-11-11-1i−ii−i11-1-11-1i−ii−i1-1i−i11-1-1−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11ii−i−ii−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ111-1−1+i321−i32−1−i321+i32ζ7−ζ7ζ11−ζ11
χ161-11-11-1i−i−ii11-1-11-1−iii−i-11−ii11-1-111-1-1−ii−iiii−i−i−ii11-1-1−ii−ii-11-11-11i−ii−i
χ171-11-11-1i−i−ii11-1-11-1−iii−i-11−ii11-1-1−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7ii−i−i−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7-111+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ7
χ181-11-11-1i−i−ii11-1-11-1−iii−i-11−ii11-1-1−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11ii−i−i−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11-111−i32−1+i321+i32−1−i32ζ7−ζ7ζ11−ζ11
χ191-11-11-1−iii−i11-1-11-1i−i−ii-11i−i11-1-111-1-1i−ii−i−i−iiii−i11-1-1i−ii−i-11-11-11−ii−ii
χ201-11-11-1−iii−i11-1-11-1i−i−ii-11i−i11-1-1−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7−i−iiii−i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7-111+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ7
χ211-11-11-1−iii−i11-1-11-1i−i−ii-11i−i11-1-1−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11−i−iiii−i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11-111−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ11
χ221-11-11-1−ii−ii11-1-11-1−ii−ii1-1−ii11-1-111-1-1−ii−ii−i−iii−ii11-1-1−ii−ii1-11-11-1−ii−ii
χ231-11-11-1−ii−ii11-1-11-1−ii−ii1-1−ii11-1-1−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7−i−iii−ii−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ71-1−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ7
χ241-11-11-1−ii−ii11-1-11-1−ii−ii1-1−ii11-1-1−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11−i−iii−ii−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ111-1−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ11
χ2522-1-12200222222-1-1-1-1000022-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-10000000000
χ2622-1-12200222222-1-1-1-1000022-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i30000-1-11+i321−i321+i321−i321+i321+i321−i321−i320000000000
χ2722-1-12200222222-1-1-1-1000022-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i30000-1-11−i321+i321−i321+i321−i321−i321+i321+i320000000000
χ2822-1-12200-2-22222-1-1110000-2-2-1-1-1-12222-2-2-2-2000011-1-1-1-111110000000000
χ2922-1-12200-2-22222-1-1110000-2-2-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i30000111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i320000000000
χ3022-1-12200-2-22222-1-1110000-2-2-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i30000111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i320000000000
χ312-2-112-2002i−2i22-2-2-11−ii00002i−2i-1-11122-2-22i−2i2i−2i0000−ii-1-111−ii−ii0000000000
χ322-2-112-2002i−2i22-2-2-11−ii00002i−2i-1-111−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ70000−ii1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ70000000000
χ332-2-112-2002i−2i22-2-2-11−ii00002i−2i-1-111−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ110000−ii1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ110000000000
χ342-2-112-200−2i2i22-2-2-11i−i0000−2i2i-1-11122-2-2−2i2i−2i2i0000i−i-1-111i−ii−i0000000000
χ352-2-112-200−2i2i22-2-2-11i−i0000−2i2i-1-111−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ70000i−i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ70000000000
χ362-2-112-200−2i2i22-2-2-11i−i0000−2i2i-1-111−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ110000i−i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ110000000000
χ373333333333-1-1-1-133333333-1-1-1-1-1-100000000-1-1-1-1-1-100000000-1-100000000
χ3833333333-3-3-1-1-1-133-3-333-3-311-1-1-1-100000000-1-1-1-111000000001100000000
χ39333333-3-333-1-1-1-13333-3-3-3-3-1-1-1-1-1-1000000001111-1-1000000001100000000
χ40333333-3-3-3-3-1-1-1-133-3-3-3-33311-1-1-1-10000000011111100000000-1-100000000
χ413-33-33-33i−3i3i−3i-1-1113-33i−3i3i−3i3-3−ii-1-11100000000−i−iii−ii00000000-1100000000
χ423-33-33-33i−3i−3i3i-1-1113-3−3i3i3i−3i-33i−i-1-11100000000−i−iiii−i000000001-100000000
χ433-33-33-3−3i3i3i−3i-1-1113-33i−3i−3i3i-33−ii-1-11100000000ii−i−i−ii000000001-100000000
χ443-33-33-3−3i3i−3i3i-1-1113-3−3i3i−3i3i3-3i−i-1-11100000000ii−i−ii−i00000000-1100000000
χ456666-2-266002i−2i2i−2i-2-200-2-200002i−2i2i−2i000000002i−2i2i−2i00000000000000000000
χ466666-2-26600−2i2i−2i2i-2-200-2-20000−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000
χ476666-2-2-6-6002i−2i2i−2i-2-2002200002i−2i2i−2i00000000−2i2i−2i2i00000000000000000000
χ486666-2-2-6-600−2i2i−2i2i-2-200220000−2i2i−2i2i000000002i−2i2i−2i00000000000000000000
χ4966-3-3660066-2-2-2-2-3-3-3-30000-2-2111100000000000011000000000000000000
χ5066-3-36600-6-6-2-2-2-2-3-3330000221111000000000000-1-1000000000000000000
χ516-66-6-226i−6i002i−2i−2i2i-2200−2i2i00002i−2i−2i2i00000000-222-200000000000000000000
χ526-66-6-226i−6i00−2i2i2i−2i-2200−2i2i0000−2i2i2i−2i000000002-2-2200000000000000000000
χ536-66-6-22−6i6i002i−2i−2i2i-22002i−2i00002i−2i−2i2i000000002-2-2200000000000000000000
χ546-66-6-22−6i6i00−2i2i2i−2i-22002i−2i0000−2i2i2i−2i00000000-222-200000000000000000000
χ556-6-336-6006i−6i-2-222-33−3i3i0000−2i2i11-1-1000000000000i−i000000000000000000
χ566-6-336-600−6i6i-2-222-333i−3i00002i−2i11-1-1000000000000−ii000000000000000000
χ571212-6-6-4-400004i−4i4i−4i2200000000−2i2i−2i2i00000000000000000000000000000000
χ581212-6-6-4-40000−4i4i−4i4i22000000002i−2i2i−2i00000000000000000000000000000000
χ5912-12-66-4400004i−4i−4i4i2-200000000−2i2i2i−2i00000000000000000000000000000000
χ6012-12-66-440000−4i4i4i−4i2-2000000002i−2i−2i2i00000000000000000000000000000000

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