Finite Group Databasebeta

← Group #72239347

Character table — Group #72239347

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size113344666666666666121212121212121212121212121248484848484848484848484848484848256256256256256256256256
order122244444444444444224444444444448888888888888888336612121212
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ42222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-20000000000000000-1-1-1-11111
χ52222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-200000000000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ62222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-200000000000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ733333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ83333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i00000000
χ93333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i00000000
χ103333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i1111111100000000
χ113333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i1111111100000000
χ12333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i00000000
χ13333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i00000000
χ14333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i1100000000
χ15333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i1100000000
χ16333333-1-1-1-1-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-1300000000
χ17333333-1-1-1-1-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-13-1-13-100000000
χ18333333-1-1-1-1-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-133-1-1-1-13-1-100000000
χ19333333-1-1-1-1-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-1-1-1-13-1-13-1-13-1-13-1-1-100000000
χ20333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-11−1+2i1−1−2i−1−2i1−1+2i1−1+2i1−1−2i11−1−2i1−1+2i00000000
χ21333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-11−1−2i1−1+2i−1+2i1−1−2i1−1−2i1−1+2i11−1+2i1−1−2i00000000
χ22333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-1−1+2i1−1−2i11−1−2i1−1+2i1−1+2i1−1−2i−1−2i1−1+2i100000000
χ23333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-1−1−2i1−1+2i11−1+2i1−1−2i1−1−2i1−1+2i−1+2i1−1−2i100000000
χ24333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1331−1+2i−1−2i1−1−2i11−1+2i1−1−2i−1+2i1−1+2i11−1−2i00000000
χ25333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1331−1−2i−1+2i1−1+2i11−1−2i1−1+2i−1−2i1−1−2i11−1+2i00000000
χ26333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133−1+2i11−1−2i1−1−2i−1+2i1−1−2i11−1+2i1−1+2i−1−2i100000000
χ27333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133−1−2i11−1+2i1−1+2i−1−2i1−1+2i11−1−2i1−1−2i−1+2i100000000
χ284-44-44i−4i4i4i−4i−4i000000004-4000000000000000000000000000011-1-1i−ii−i
χ294-44-44i−4i4i4i−4i−4i000000004-40000000000000000000000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7
χ304-44-44i−4i4i4i−4i−4i000000004-40000000000000000000000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11
χ314-44-4−4i4i−4i−4i4i4i000000004-4000000000000000000000000000011-1-1−ii−ii
χ324-44-4−4i4i−4i−4i4i4i000000004-40000000000000000000000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7
χ334-44-4−4i4i−4i−4i4i4i000000004-40000000000000000000000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11
χ346666-6-6222266662222-2-2-2-2-2-2-2-2-6-62222000000000000000000000000
χ356666-6-62222-2-2-2-22222-2-2-2-266-2-222-6-622000000000000000000000000
χ366666-6-62222-2-2-2-22222-2-2-2-2-2-2662222-6-6000000000000000000000000
χ376666-6-62222-2-2-2-2-6-6-6-6-2-266-2-2-2-2222222000000000000000000000000
χ386666-6-6-6-6-6-6-2-2-2-2222266-2-2-2-2-2-2222222000000000000000000000000
χ391212-4-4004-44-444−4+8i−4−8i4i4i−4i−4i00000000004-44i−4i000000000000000000000000
χ401212-4-4004-44-444−4−8i−4+8i−4i−4i4i4i00000000004-4−4i4i000000000000000000000000
χ411212-4-4004-44-4−4+8i−4−8i444i4i−4i−4i0000000000-44−4i4i000000000000000000000000
χ421212-4-4004-44-4−4−8i−4+8i44−4i−4i4i4i0000000000-444i−4i000000000000000000000000
χ431212-4-400-44-4444−4+8i−4−8i−4i−4i4i4i0000000000-44−4i4i000000000000000000000000
χ441212-4-400-44-4444−4−8i−4+8i4i4i−4i−4i0000000000-444i−4i000000000000000000000000
χ451212-4-400-44-44−4+8i−4−8i44−4i−4i4i4i00000000004-44i−4i000000000000000000000000
χ461212-4-400-44-44−4−8i−4+8i444i4i−4i−4i00000000004-4−4i4i000000000000000000000000
χ4712-1212-1212i−12i−4i−4i4i4i00000000-44000000000000000000000000000000000000
χ4812-1212-12−12i12i4i4i−4i−4i00000000-44000000000000000000000000000000000000
χ4912-12-44004i−4i−4i4i00004+4i−4−4i4−4i−4+4i004i−4i4i−4i4-44-40000000000000000000000000000
χ5012-12-44004i−4i−4i4i00004−4i−4+4i4+4i−4−4i00−4i4i4i−4i-44-440000000000000000000000000000
χ5112-12-44004i−4i−4i4i0000−4+4i4−4i−4−4i4+4i00−4i4i−4i4i4-4-440000000000000000000000000000
χ5212-12-44004i−4i−4i4i0000−4−4i4+4i−4+4i4−4i004i−4i−4i4i-444-40000000000000000000000000000
χ5312-12-4400−4i4i4i−4i00004+4i−4−4i4−4i−4+4i004i−4i−4i4i-44-440000000000000000000000000000
χ5412-12-4400−4i4i4i−4i00004−4i−4+4i4+4i−4−4i00−4i4i−4i4i4-44-40000000000000000000000000000
χ5512-12-4400−4i4i4i−4i0000−4+4i4−4i−4−4i4+4i00−4i4i4i−4i-444-40000000000000000000000000000
χ5612-12-4400−4i4i4i−4i0000−4−4i4+4i−4+4i4−4i004i−4i4i−4i4-4-440000000000000000000000000000

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