Finite Group Databasebeta

← Group #11922553

Character table — Group #11922553

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1133333333333344449999999999121212121212121212121212121212121212121216161616484848486464646464646464
order12222244444444336622444444446666121212121212121212121212121212123366666633336666
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−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−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411111111111111−1−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−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ511111111111111−1−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−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i3211−1−i32
χ611111111111111−1−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−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1−i32−1+i3211−1−i32−1+i321
χ711111111111111−1+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+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ811111111111111−1+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+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1+i32−1−i3211−1+i32−1−i321
χ911111111111111−1+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+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i3211−1+i32
χ101-11-1-111111-1-1-1-111-1-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11-11-11111-1-1-1-1
χ111-11-1-111111-1-1-1-111-1-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ121-11-1-111111-1-1-1-111-1-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ131-11-1-111111-1-1-1-1−1−i32−1+i321+i321−i321-11111-1-1-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3211-1-11-11-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ141-11-1-111111-1-1-1-1−1−i32−1+i321+i321−i321-11111-1-1-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1+i3211−1−i321−i32-1-11+i32
χ151-11-1-111111-1-1-1-1−1−i32−1+i321+i321−i321-11111-1-1-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i321−1−i32−1+i321-11+i321−i32-1
χ161-11-1-111111-1-1-1-1−1+i32−1−i321−i321+i321-11111-1-1-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211-1-11-11-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ171-11-1-111111-1-1-1-1−1+i32−1−i321−i321+i321-11111-1-1-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i321−1+i32−1−i321-11−i321+i32-1
χ181-11-1-111111-1-1-1-1−1+i32−1−i321−i321+i321-11111-1-1-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1−i3211−1+i321+i32-1-11−i32
χ19333333-1-1-1-1-1-1-1-1333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20333333-1-1-1-1-1-1-1-1−3−3i32−3+3i32−3−3i32−3+3i3233-1-1-1-1-1-1-1-1−3−3i32−3+3i32−3−3i32−3+3i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i320000000000000000
χ21333333-1-1-1-1-1-1-1-1−3+3i32−3−3i32−3+3i32−3−3i3233-1-1-1-1-1-1-1-1−3+3i32−3−3i32−3+3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i320000000000000000
χ223333-1-111−1+2i−1−2i11−1+2i−1−2i3333-1-111−1+2i−1−2i11−1+2i−1−2i-1-1-1-111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i0000000000000000
χ233333-1-111−1+2i−1−2i11−1+2i−1−2i−3−3i32−3+3i32−3−3i32−3+3i32-1-111−1+2i−1−2i11−1+2i−1−2i1+i321−i321+i321−i32−1−i32−1−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32ζ2+2ζ11ζ2−2ζ11−1+i32−1+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i322ζ7+ζ10−2ζ7+ζ100000000000000000
χ243333-1-111−1+2i−1−2i11−1+2i−1−2i−3+3i32−3−3i32−3+3i32−3−3i32-1-111−1+2i−1−2i11−1+2i−1−2i1−i321+i321−i321+i32−1+i32−1+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i322ζ7+ζ10−2ζ7+ζ10−1−i32−1−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32ζ2+2ζ11ζ2−2ζ110000000000000000
χ253333-1-111−1−2i−1+2i11−1−2i−1+2i3333-1-111−1−2i−1+2i11−1−2i−1+2i-1-1-1-111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i0000000000000000
χ263333-1-111−1−2i−1+2i11−1−2i−1+2i−3−3i32−3+3i32−3−3i32−3+3i32-1-111−1−2i−1+2i11−1−2i−1+2i1+i321−i321+i321−i32−1−i32−1−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32ζ2−2ζ11ζ2+2ζ11−1+i32−1+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i32−2ζ7+ζ102ζ7+ζ100000000000000000
χ273333-1-111−1−2i−1+2i11−1−2i−1+2i−3+3i32−3−3i32−3+3i32−3−3i32-1-111−1−2i−1+2i11−1−2i−1+2i1−i321+i321−i321+i32−1+i32−1+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i32−2ζ7+ζ102ζ7+ζ10−1−i32−1−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32ζ2−2ζ11ζ2+2ζ110000000000000000
χ283333-1-1−1+2i−1−2i11−1+2i−1−2i113333-1-1−1+2i−1−2i11−1+2i−1−2i11-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i110000000000000000
χ293333-1-1−1+2i−1−2i11−1+2i−1−2i11−3−3i32−3+3i32−3−3i32−3+3i32-1-1−1+2i−1−2i11−1+2i−1−2i111+i321−i321+i321−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i320000000000000000
χ303333-1-1−1+2i−1−2i11−1+2i−1−2i11−3+3i32−3−3i32−3+3i32−3−3i32-1-1−1+2i−1−2i11−1+2i−1−2i111−i321+i321−i321+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i320000000000000000
χ313333-1-1−1−2i−1+2i11−1−2i−1+2i113333-1-1−1−2i−1+2i11−1−2i−1+2i11-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i110000000000000000
χ323333-1-1−1−2i−1+2i11−1−2i−1+2i11−3−3i32−3+3i32−3−3i32−3+3i32-1-1−1−2i−1+2i11−1−2i−1+2i111+i321−i321+i321−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i320000000000000000
χ333333-1-1−1−2i−1+2i11−1−2i−1+2i11−3+3i32−3−3i32−3+3i32−3−3i32-1-1−1−2i−1+2i11−1−2i−1+2i111−i321+i321−i321+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i320000000000000000
χ3433-1-133333333330000-1-1-1-1-1-1-1-1-1-1000000000000000000003333-1-1-1-100000000
χ3533-1-133333333330000-1-1-1-1-1-1-1-1-1-100000000000000000000−3−3i32−3+3i32−3−3i32−3+3i321+i321+i321−i321−i3200000000
χ3633-1-133333333330000-1-1-1-1-1-1-1-1-1-100000000000000000000−3+3i32−3−3i32−3+3i32−3−3i321−i321−i321+i321+i3200000000
χ373-33-31-111−1+2i−1−2i-1-11−2i1+2i33-3-3-1111−1+2i−1−2i-1-11−2i1+2i11-1-111−1+2i−1−2i-1-11−2i1+2i11−1+2i−1−2i-1-11−2i1+2i0000000000000000
χ383-33-31-111−1+2i−1−2i-1-11−2i1+2i−3−3i32−3+3i323+3i323−3i32-1111−1+2i−1−2i-1-11−2i1+2i−1−i32−1+i321+i321−i32−1−i32−1−i32ζ2+2ζ11ζ2−2ζ111+i321+i32−ζ2−2ζ11−ζ2+2ζ11−1+i32−1+i322ζ7+ζ10−2ζ7+ζ101−i321−i32−2ζ7−ζ102ζ7−ζ100000000000000000
χ393-33-31-111−1+2i−1−2i-1-11−2i1+2i−3+3i32−3−3i323−3i323+3i32-1111−1+2i−1−2i-1-11−2i1+2i−1+i32−1−i321−i321+i32−1+i32−1+i322ζ7+ζ10−2ζ7+ζ101−i321−i32−2ζ7−ζ102ζ7−ζ10−1−i32−1−i32ζ2+2ζ11ζ2−2ζ111+i321+i32−ζ2−2ζ11−ζ2+2ζ110000000000000000
χ403-33-31-111−1−2i−1+2i-1-11+2i1−2i33-3-3-1111−1−2i−1+2i-1-11+2i1−2i11-1-111−1−2i−1+2i-1-11+2i1−2i11−1−2i−1+2i-1-11+2i1−2i0000000000000000
χ413-33-31-111−1−2i−1+2i-1-11+2i1−2i−3−3i32−3+3i323+3i323−3i32-1111−1−2i−1+2i-1-11+2i1−2i−1−i32−1+i321+i321−i32−1−i32−1−i32ζ2−2ζ11ζ2+2ζ111+i321+i32−ζ2+2ζ11−ζ2−2ζ11−1+i32−1+i32−2ζ7+ζ102ζ7+ζ101−i321−i322ζ7−ζ10−2ζ7−ζ100000000000000000
χ423-33-31-111−1−2i−1+2i-1-11+2i1−2i−3+3i32−3−3i323−3i323+3i32-1111−1−2i−1+2i-1-11+2i1−2i−1+i32−1−i321−i321+i32−1+i32−1+i32−2ζ7+ζ102ζ7+ζ101−i321−i322ζ7−ζ10−2ζ7−ζ10−1−i32−1−i32ζ2−2ζ11ζ2+2ζ111+i321+i32−ζ2+2ζ11−ζ2−2ζ110000000000000000
χ433-33-31-1−1+2i−1−2i111−2i1+2i-1-133-3-3-11−1+2i−1−2i111−2i1+2i-1-111-1-1−1+2i−1−2i111−2i1+2i-1-1−1+2i−1−2i111−2i1+2i-1-10000000000000000
χ443-33-31-1−1+2i−1−2i111−2i1+2i-1-1−3−3i32−3+3i323+3i323−3i32-11−1+2i−1−2i111−2i1+2i-1-1−1−i32−1+i321+i321−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32−ζ2−2ζ11−ζ2+2ζ111+i321+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i32−2ζ7−ζ102ζ7−ζ101−i321−i320000000000000000
χ453-33-31-1−1+2i−1−2i111−2i1+2i-1-1−3+3i32−3−3i323−3i323+3i32-11−1+2i−1−2i111−2i1+2i-1-1−1+i32−1−i321−i321+i322ζ7+ζ10−2ζ7+ζ10−1+i32−1+i32−2ζ7−ζ102ζ7−ζ101−i321−i32ζ2+2ζ11ζ2−2ζ11−1−i32−1−i32−ζ2−2ζ11−ζ2+2ζ111+i321+i320000000000000000
χ463-33-31-1−1−2i−1+2i111+2i1−2i-1-133-3-3-11−1−2i−1+2i111+2i1−2i-1-111-1-1−1−2i−1+2i111+2i1−2i-1-1−1−2i−1+2i111+2i1−2i-1-10000000000000000
χ473-33-31-1−1−2i−1+2i111+2i1−2i-1-1−3−3i32−3+3i323+3i323−3i32-11−1−2i−1+2i111+2i1−2i-1-1−1−i32−1+i321+i321−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32−ζ2+2ζ11−ζ2−2ζ111+i321+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i322ζ7−ζ10−2ζ7−ζ101−i321−i320000000000000000
χ483-33-31-1−1−2i−1+2i111+2i1−2i-1-1−3+3i32−3−3i323−3i323+3i32-11−1−2i−1+2i111+2i1−2i-1-1−1+i32−1−i321−i321+i32−2ζ7+ζ102ζ7+ζ10−1+i32−1+i322ζ7−ζ10−2ζ7−ζ101−i321−i32ζ2−2ζ11ζ2+2ζ11−1−i32−1−i32−ζ2+2ζ11−ζ2−2ζ111+i321+i320000000000000000
χ493-33-3-33-1-1-1-1111133-3-33-3-1-1-1-11111-3-333-1-1-1-11111-1-1-1-111110000000000000000
χ503-33-3-33-1-1-1-11111−3−3i32−3+3i323+3i323−3i323-3-1-1-1-111113+3i323−3i32−3−3i32−3+3i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i320000000000000000
χ513-33-3-33-1-1-1-11111−3+3i32−3−3i323−3i323+3i323-3-1-1-1-111113−3i323+3i32−3+3i32−3−3i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i320000000000000000
χ523-3-11-333333-3-3-3-30000-11-1-1-1-111110000000000000000000033-3-3-11-1100000000
χ533-3-11-333333-3-3-3-30000-11-1-1-1-1111100000000000000000000−3−3i32−3+3i323+3i323−3i321+i32−1−i321−i32−1+i3200000000
χ543-3-11-333333-3-3-3-30000-11-1-1-1-1111100000000000000000000−3+3i32−3−3i323−3i323+3i321−i32−1+i321+i32−1−i3200000000
χ5599-3-399-3-3-3-3-3-3-3-30000-3-311111111000000000000000000000000000000000000
χ5699-3-3-3-333−3+6i−3−6i33−3+6i−3−6i000011-1-11−2i1+2i-1-11−2i1+2i000000000000000000000000000000000000
χ5799-3-3-3-333−3−6i−3+6i33−3−6i−3+6i000011-1-11+2i1−2i-1-11+2i1−2i000000000000000000000000000000000000
χ5899-3-3-3-3−3+6i−3−6i33−3+6i−3−6i330000111−2i1+2i-1-11−2i1+2i-1-1000000000000000000000000000000000000
χ5999-3-3-3-3−3−6i−3+6i33−3−6i−3+6i330000111+2i1−2i-1-11+2i1−2i-1-1000000000000000000000000000000000000
χ609-9-333-333−3+6i−3−6i-3-33−6i3+6i00001-1-1-11−2i1+2i11−1+2i−1−2i000000000000000000000000000000000000
χ619-9-333-333−3−6i−3+6i-3-33+6i3−6i00001-1-1-11+2i1−2i11−1−2i−1+2i000000000000000000000000000000000000
χ629-9-333-3−3+6i−3−6i333−6i3+6i-3-300001-11−2i1+2i-1-1−1+2i−1−2i11000000000000000000000000000000000000
χ639-9-333-3−3−6i−3+6i333+6i3−6i-3-300001-11+2i1−2i-1-1−1−2i−1+2i11000000000000000000000000000000000000
χ649-9-33-99-3-3-3-333330000-331111-1-1-1-1000000000000000000000000000000000000

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