Finite Group Databasebeta

← Group #73175

Character table — Group #73175

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111111122222222222244444444444444446666888888888888888888888888121212121212
order1222222244444444444433666666666666664444121212121212121212121212121212121212121212121212224444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111−1−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+i321111−1−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+i32111111
χ311111111111111111111−1+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−i321111−1+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−i32111111
χ4111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ5111111111111-1-1-1-1-1-1-1-1−1−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+i321111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32-1-111-1-1
χ6111111111111-1-1-1-1-1-1-1-1−1+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−i321111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32-1-111-1-1
χ711111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ811111111-1-1-1-11111-1-1-1-1−1−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+i3211111+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1-1-111
χ911111111-1-1-1-11111-1-1-1-1−1+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−i3211111−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1-1-111
χ1011111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ1111111111-1-1-1-1-1-1-1-11111−1−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+i3211111+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i3211-1-1-1-1
χ1211111111-1-1-1-1-1-1-1-11111−1+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−i3211111−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i3211-1-1-1-1
χ13111-1-1-1-11ii−i−iii−i−i11-1-11111-1-111-1-11-1-11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−i
χ14111-1-1-1-11ii−i−iii−i−i11-1-1−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i321-1i−ii−i
χ15111-1-1-1-11ii−i−iii−i−i11-1-1−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i321-1i−ii−i
χ16111-1-1-1-11ii−i−i−i−iii-1-1111111-1-111-1-11-1-11-1-111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111-11i−i−ii
χ17111-1-1-1-11ii−i−i−i−iii-1-111−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32-11i−i−ii
χ18111-1-1-1-11ii−i−i−i−iii-1-111−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32-11i−i−ii
χ19111-1-1-1-11−i−iiiii−i−i-1-1111111-1-111-1-11-1-11-1-111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111-11−iii−i
χ20111-1-1-1-11−i−iiiii−i−i-1-111−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32-11−iii−i
χ21111-1-1-1-11−i−iiiii−i−i-1-111−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32-11−iii−i
χ22111-1-1-1-11−i−iii−i−iii11-1-11111-1-111-1-11-1-11-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-11-1−ii−ii
χ23111-1-1-1-11−i−iii−i−iii11-1-1−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i321-1−ii−ii
χ24111-1-1-1-11−i−iii−i−iii11-1-1−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i321-1−ii−ii
χ2522-22-22-2-22-22-22i−2i2i−2i2i−2i2i−2i-1-11-11-11-11-111-111-100001-11-1i−ii−ii−ii−i1-11-1i−ii−ii−ii−i000000
χ2622-22-22-2-22-22-22i−2i2i−2i2i−2i2i−2i1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i320000−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7000000
χ2722-22-22-2-22-22-22i−2i2i−2i2i−2i2i−2i1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i320000−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11000000
χ2822-22-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i-1-11-11-11-11-111-111-100001-11-1−ii−ii−ii−ii1-11-1−ii−ii−ii−ii000000
χ2922-22-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i320000−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7000000
χ3022-22-22-2-22-22-2−2i2i−2i2i−2i2i−2i2i1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i320000−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11000000
χ3122-22-22-2-2-22-222i−2i2i−2i−2i2i−2i2i-1-11-11-11-11-111-111-10000-11-11i−ii−i−ii−ii-11-11i−ii−i−ii−ii000000
χ3222-22-22-2-2-22-222i−2i2i−2i−2i2i−2i2i1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i3200001+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ111−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7000000
χ3322-22-22-2-2-22-222i−2i2i−2i−2i2i−2i2i1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i3200001−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ71+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11000000
χ3422-22-22-2-2-22-22−2i2i−2i2i2i−2i2i−2i-1-11-11-11-11-111-111-10000-11-11−ii−iii−ii−i-11-11−ii−iii−ii−i000000
χ3522-22-22-2-2-22-22−2i2i−2i2i2i−2i2i−2i1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i3200001+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ111−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7000000
χ3622-22-22-2-2-22-22−2i2i−2i2i2i−2i2i−2i1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i3200001−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ71+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11000000
χ3722-2-22-22-22i−2i−2i2i2-2-22−2i2i2i−2i-1-11-1-111-1-111-111-110000i−i−ii1-1-11−iii−ii−i−ii1-1-11−iii−i000000
χ3822-2-22-22-22i−2i−2i2i2-2-22−2i2i2i−2i1+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i320000ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7000000
χ3922-2-22-22-22i−2i−2i2i2-2-22−2i2i2i−2i1−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i320000ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11000000
χ4022-2-22-22-22i−2i−2i2i-222-22i−2i−2i2i-1-11-1-111-1-111-111-110000i−i−ii-111-1i−i−iii−i−ii-111-1i−i−ii000000
χ4122-2-22-22-22i−2i−2i2i-222-22i−2i−2i2i1+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i320000ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7000000
χ4222-2-22-22-22i−2i−2i2i-222-22i−2i−2i2i1−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i320000ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11000000
χ4322-2-22-22-2−2i2i2i−2i2-2-222i−2i−2i2i-1-11-1-111-1-111-111-110000−iii−i1-1-11i−i−ii−iii−i1-1-11i−i−ii000000
χ4422-2-22-22-2−2i2i2i−2i2-2-222i−2i−2i2i1+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i320000−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7000000
χ4522-2-22-22-2−2i2i2i−2i2-2-222i−2i−2i2i1−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i320000−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11000000
χ4622-2-22-22-2−2i2i2i−2i-222-2−2i2i2i−2i-1-11-1-111-1-111-111-110000−iii−i-111-1−iii−i−iii−i-111-1−iii−i000000
χ4722-2-22-22-2−2i2i2i−2i-222-2−2i2i2i−2i1+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i320000−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7000000
χ4822-2-22-22-2−2i2i2i−2i-222-2−2i2i2i−2i1−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i320000−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11000000
χ492-2-22-2-22200000000000022-2-22-2-2-22-22-222-222-22-2000000000000000000000000000000
χ502-2-22-2-222000000000000−1−i3−1+i31+i31+i3−1−i31+i31−i31−i3−1+i31−i3−1−i31+i3−1−i3−1+i31−i3−1+i32-22-2000000000000000000000000000000
χ512-2-22-2-222000000000000−1+i3−1−i31−i31−i3−1+i31−i31+i31+i3−1−i31+i3−1+i31−i3−1+i3−1−i31+i3−1−i32-22-2000000000000000000000000000000
χ522-2-2-222-2200000000000022-2-2-22-2-2-2222-222-22-2-22000000000000000000000000000000
χ532-2-2-222-22000000000000−1−i3−1+i31+i31+i31+i3−1−i31−i31−i31−i3−1+i3−1−i3−1−i31+i3−1+i3−1+i31−i32-2-22000000000000000000000000000000
χ542-2-2-222-22000000000000−1+i3−1−i31−i31−i31−i3−1+i31+i31+i31+i3−1−i3−1+i3−1+i31−i3−1−i3−1−i31+i32-2-22000000000000000000000000000000
χ55333333333333333333330000000000000000-1-1-1-1000000000000000000000000-1-1-1-1-1-1
χ56333333333333-3-3-3-3-3-3-3-30000000000000000-1-1-1-100000000000000000000000011-1-111
χ5733333333-3-3-3-33333-3-3-3-30000000000000000-1-1-1-10000000000000000000000001111-1-1
χ5833333333-3-3-3-3-3-3-3-333330000000000000000-1-1-1-1000000000000000000000000-1-11111
χ59333-3-3-3-333i3i−3i−3i3i3i−3i−3i33-3-30000000000000000-1-111000000000000000000000000-11−ii−ii
χ60333-3-3-3-333i3i−3i−3i−3i−3i3i3i-3-3330000000000000000-1-1110000000000000000000000001-1−iii−i
χ61333-3-3-3-33−3i−3i3i3i3i3i−3i−3i-3-3330000000000000000-1-1110000000000000000000000001-1i−i−ii
χ62333-3-3-3-33−3i−3i3i3i−3i−3i3i3i33-3-30000000000000000-1-111000000000000000000000000-11i−ii−i
χ634-4444-4-4-4000000000000-2-2-2222-22222-2-22-2-20000000000000000000000000000000000
χ644-4444-4-4-40000000000001+i31−i31+i3−1−i3−1−i3−1−i31−i3−1+i3−1+i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000000000000000000000000000000000
χ654-4444-4-4-40000000000001−i31+i31−i3−1+i3−1+i3−1+i31+i3−1−i3−1−i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000000000000000000000000000000000
χ664-44-4-444-4000000000000-2-2-22-2-2-22-2-22222220000000000000000000000000000000000
χ674-44-4-444-40000000000001+i31−i31+i3−1−i31+i31+i31−i3−1+i31−i31−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000000000000000000000000000000
χ684-44-4-444-40000000000001−i31+i31−i3−1+i31−i31−i31+i3−1−i31+i31+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000000000000000000000000000000
χ696-6-66-6-6660000000000000000000000000000-22-22000000000000000000000000000000
χ706-6-6-666-660000000000000000000000000000-222-2000000000000000000000000000000

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