Finite Group Databasebeta

← Group #73177

Character table — Group #73177

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111111122222222222244444444444444446666888888888888888888888888121212121212
order1222222244444444444433666666666666664444121212121212121212121212121212121212121212121212444444
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
χ4111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
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−i3211-1-1-1-1
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+i3211-1-1-1-1
χ711111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
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−i32-1-111-1-1
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+i32-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
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+i32-1-1-1-111
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−i32-1-1-1-111
χ131-1-1111-1-111-1-1ii−i−iii−i−i1111-1-111-1-11-1-11-1-111-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1-1i−ii−i
χ141-1-1111-1-111-1-1ii−i−iii−i−i−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ71-1i−ii−i
χ151-1-1111-1-111-1-1ii−i−iii−i−i−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ111-1i−ii−i
χ161-1-1111-1-111-1-1−i−iii−i−iii1111-1-111-1-11-1-11-1-111-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1-1−ii−ii
χ171-1-1111-1-111-1-1−i−iii−i−iii−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ71-1−ii−ii
χ181-1-1111-1-111-1-1−i−iii−i−iii−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ111-1−ii−ii
χ191-1-1111-1-1-1-111ii−i−i−i−iii1111-1-111-1-11-1-11-1-111-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-11i−i−ii
χ201-1-1111-1-1-1-111ii−i−i−i−iii−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-11+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7-11i−i−ii
χ211-1-1111-1-1-1-111ii−i−i−i−iii−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-11−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11-11i−i−ii
χ221-1-1111-1-1-1-111−i−iiiii−i−i1111-1-111-1-11-1-11-1-111-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i-11−iii−i
χ231-1-1111-1-1-1-111−i−iiiii−i−i−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-11+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7-11−iii−i
χ241-1-1111-1-1-1-111−i−iiiii−i−i−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-11−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11-11−iii−i
χ25222-22-2-2-2000000000000222-2222-222-2-2-2-2-2-22-22-2000000000000000000000000000000
χ26222-22-2-2-2000000000000−1−i3−1+i3−1−i31+i3−1−i3−1−i3−1+i31−i3−1+i3−1+i31+i31+i31+i31−i31−i31−i32-22-2000000000000000000000000000000
χ27222-22-2-2-2000000000000−1+i3−1−i3−1+i31−i3−1+i3−1+i3−1−i31+i3−1−i3−1−i31−i31−i31−i31+i31+i31+i32-22-2000000000000000000000000000000
χ2822-2-2-222-22i−2i2i−2i2-22-22i−2i2i−2i-1-11-11-11-11-111-111-10000i−ii−i1-11-1i−ii−ii−ii−i1-11-1i−ii−i000000
χ2922-2-2-222-22i−2i2i−2i2-22-22i−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−i320000ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7000000
χ3022-2-2-222-22i−2i2i−2i2-22-22i−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+i320000ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11000000
χ3122-2-2-222-22i−2i2i−2i-22-22−2i2i−2i2i-1-11-11-11-11-111-111-10000i−ii−i-11-11−ii−iii−ii−i-11-11−ii−ii000000
χ3222-2-2-222-22i−2i2i−2i-22-22−2i2i−2i2i1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i320000ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7000000
χ3322-2-2-222-22i−2i2i−2i-22-22−2i2i−2i2i1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i320000ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11000000
χ3422-2-2-222-2−2i2i−2i2i2-22-2−2i2i−2i2i-1-11-11-11-11-111-111-10000−ii−ii1-11-1−ii−ii−ii−ii1-11-1−ii−ii000000
χ3522-2-2-222-2−2i2i−2i2i2-22-2−2i2i−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−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7000000
χ3622-2-2-222-2−2i2i−2i2i2-22-2−2i2i−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−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11000000
χ3722-2-2-222-2−2i2i−2i2i-22-222i−2i2i−2i-1-11-11-11-11-111-111-10000−ii−ii-11-11i−ii−i−ii−ii-11-11i−ii−i000000
χ3822-2-2-222-2−2i2i−2i2i-22-222i−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−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7000000
χ3922-2-2-222-2−2i2i−2i2i-22-222i−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−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11000000
χ402-22-2-22-222i−2i−2i2i2i−2i−2i2i-222-2-1-11-1-111-1-111-111-110000i−i−iii−i−ii-111-1i−i−iii−i−ii-111-1000000
χ412-22-2-22-222i−2i−2i2i2i−2i−2i2i-222-21+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−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32000000
χ422-22-2-22-222i−2i−2i2i2i−2i−2i2i-222-21−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−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32000000
χ432-22-2-22-222i−2i−2i2i−2i2i2i−2i2-2-22-1-11-1-111-1-111-111-110000i−i−ii−iii−i1-1-11i−i−ii−iii−i1-1-11000000
χ442-22-2-22-222i−2i−2i2i−2i2i2i−2i2-2-221+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−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32000000
χ452-22-2-22-222i−2i−2i2i−2i2i2i−2i2-2-221−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−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32000000
χ462-22-2-22-22−2i2i2i−2i2i−2i−2i2i2-2-22-1-11-1-111-1-111-111-110000−iii−ii−i−ii1-1-11−iii−ii−i−ii1-1-11000000
χ472-22-2-22-22−2i2i2i−2i2i−2i−2i2i2-2-221+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−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32000000
χ482-22-2-22-22−2i2i2i−2i2i−2i−2i2i2-2-221−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−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32000000
χ492-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222-2-1-11-1-111-1-111-111-110000−iii−i−iii−i-111-1−iii−i−iii−i-111-1000000
χ502-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222-21+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−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32000000
χ512-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222-21−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−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32000000
χ522-2-2-22-222000000000000222-2-2-22-2-2-2-222-2222-2-22000000000000000000000000000000
χ532-2-2-22-222000000000000−1−i3−1+i3−1−i31+i31+i31+i3−1+i31−i31−i31−i31+i3−1−i3−1−i31−i3−1+i3−1+i32-2-22000000000000000000000000000000
χ542-2-2-22-222000000000000−1+i3−1−i3−1+i31−i31−i31−i3−1−i31+i31+i31+i31−i3−1+i3−1+i31+i3−1−i3−1−i32-2-22000000000000000000000000000000
χ55333333333333333333330000000000000000-1-1-1-1000000000000000000000000-1-1-1-1-1-1
χ56333333333333-3-3-3-3-3-3-3-30000000000000000-1-1-1-1000000000000000000000000-1-11111
χ5733333333-3-3-3-33333-3-3-3-30000000000000000-1-1-1-100000000000000000000000011-1-111
χ5833333333-3-3-3-3-3-3-3-333330000000000000000-1-1-1-10000000000000000000000001111-1-1
χ593-3-3333-3-333-3-33i3i−3i−3i3i3i−3i−3i0000000000000000-1-111000000000000000000000000-11−ii−ii
χ603-3-3333-3-333-3-3−3i−3i3i3i−3i−3i3i3i0000000000000000-1-111000000000000000000000000-11i−ii−i
χ613-3-3333-3-3-3-3333i3i−3i−3i−3i−3i3i3i0000000000000000-1-1110000000000000000000000001-1−iii−i
χ623-3-3333-3-3-3-333−3i−3i3i3i3i3i−3i−3i0000000000000000-1-1110000000000000000000000001-1i−i−ii
χ6344-44-4-4-44000000000000-2-2222-2222-2-2-22-2-220000000000000000000000000000000000
χ6444-44-4-4-440000000000001+i31−i3−1−i3−1−i3−1−i31+i3−1+i3−1+i3−1+i31−i31+i31+i3−1−i31−i31−i3−1+i30000000000000000000000000000000000
χ6544-44-4-4-440000000000001−i31+i3−1+i3−1+i3−1+i31−i3−1−i3−1−i3−1−i31+i31−i31−i3−1+i31+i31+i3−1−i30000000000000000000000000000000000
χ664-444-4-44-4000000000000-2-222-2222-22-22-2-22-20000000000000000000000000000000000
χ674-444-4-44-40000000000001+i31−i3−1−i3−1−i31+i3−1−i3−1+i3−1+i31−i3−1+i31+i3−1−i31+i31−i3−1+i31−i30000000000000000000000000000000000
χ684-444-4-44-40000000000001−i31+i3−1+i3−1+i31−i3−1+i3−1−i3−1−i31+i3−1−i31−i3−1+i31−i31+i3−1−i31+i30000000000000000000000000000000000
χ69666-66-6-6-60000000000000000000000000000-22-22000000000000000000000000000000
χ706-6-6-66-6660000000000000000000000000000-222-2000000000000000000000000000000

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