Finite Group Databasebeta

← Group #72275050

Character table — Group #72275050

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222244666688888121212121212161616161616161618182424242424242424323232323232323232323232323232323232323236363636484872729696969696969696
order123461212222224466121222446123366666622224466121233666666121212121212121212121212224412124466666666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+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
χ3111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−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
χ4111111111-1-1111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ5111111111-1-11111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−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+i32-1-1-1-111-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ6111111111-1-11111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+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−i32-1-1-1-111-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ71111111-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-11-111-1-111-1-11111-1-1-1-111-1-111-1-1
χ81111111-1-11111-1-1-1-1-1111111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-1-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321111-1-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ91111111-1-11111-1-1-1-1-1111111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-1-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321111-1-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ101111111-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-1111-11-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111-1-1-1-111-1-1-1-1-1111111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-111-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1-1-1-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ121111111-1-1-1-111-1-1-1-1-1111111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-111-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1-1-1-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ13111-11-1-1111-11-1-111-1-11-11-11-1111111111-11-11-11-11-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11-11-11-1
χ14111-11-1-1111-11-1-111-1-11-11-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11-11-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321-11-11-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ15111-11-1-1111-11-1-111-1-11-11-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11-11-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321-11-11-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ16111-11-1-111-111-1-111-1-11-11-11-111111111-11-111-11-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11-11-11-11
χ17111-11-1-111-111-1-111-1-11-11-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11-111-11-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-11-111-1-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ18111-11-1-111-111-1-111-1-11-11-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11-111-11-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-11-111-1-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ19111-11-1-1-1-11-11-11-1-1111-11-11-111-1-1-1-1111-1-11-111-11-111-1-1-1-111-11-11-1-111-1-1111-11-1-11-111-1-111-1-11
χ20111-11-1-1-1-11-11-11-1-1111-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-11-111-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11-1-11-11−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ21111-11-1-1-1-11-11-11-1-1111-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-11-111-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11-1-11-11−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
χ22111-11-1-1-1-1-111-11-1-1111-11-11-111-1-1-1-111-111-1-111-11-111-1-1-1-111-11-11-1-111-1-111-11-11-111-1-111-1-111-1
χ23111-11-1-1-1-1-111-11-1-1111-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-111-1-111-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-11-111-11+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ24111-11-1-1-1-1-111-11-1-1111-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-111-1-111-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-11-111-11−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ2522-12-1-1-12200222-1-1-1-12222-1-122222222000022-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-1-10000000000
χ2622-12-1-1-12200222-1-1-1-12222-1-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3000022-1-1-1-11+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000-1-10000000000
χ2722-12-1-1-12200222-1-1-1-12222-1-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3000022-1-1-1-11−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000-1-10000000000
χ2822-12-1-1-1-2-20022-211112222-1-122-2-2-2-2220000-2-2-1-1-1-1-1-11111-1-12-22-2-1-111-1-1110000110000000000
χ2922-12-1-1-1-2-20022-211112222-1-1−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000-2-2-1-1-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i31+i3−1+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i320000110000000000
χ3022-12-1-1-1-2-20022-211112222-1-1−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000-2-2-1-1-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i31−i3−1−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i320000110000000000
χ3122-1-2-11122002-2-2-1-1112-22-2-112222222200002-2-11-11-1-1-1-1-1-1-1-1-2-2-2-2111111110000-110000000000
χ3222-1-2-11122002-2-2-1-1112-22-2-11−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300002-2-11-111+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000-110000000000
χ3322-1-2-11122002-2-2-1-1112-22-2-11−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300002-2-11-111−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000-110000000000
χ3422-1-2-111-2-2002-2211-1-12-22-2-1122-2-2-2-2220000-22-11-11-1-11111-1-1-22-2211-1-111-1-100001-10000000000
χ3522-1-2-111-2-2002-2211-1-12-22-2-11−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000-22-11-111+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i3−1−i31−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200001-10000000000
χ3622-1-2-111-2-2002-2211-1-12-22-2-11−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000-22-11-111−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i3−1+i31+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200001-10000000000
χ37333333333333333333-1-1-1-133000000003333-1-1-1-1-1-100000000000000000000-1-1-1-1-1-1-1-100000000
χ38333333333-3-33333333-1-1-1-13300000000-3-3-3-3-1-1-1-1-1-1000000000000000000001111-1-11100000000
χ393333333-3-33333-3-3-3-3-3-1-1-1-1330000000033-3-311-1-1-1-100000000000000000000-1-1-1-1111100000000
χ403333333-3-3-3-333-3-3-3-3-3-1-1-1-13300000000-3-33311-1-1-1-100000000000000000000111111-1-100000000
χ41333-33-3-3333-33-3-333-3-3-11-113-3000000003-33-3-11-11-1100000000000000000000-11-11-11-1100000000
χ42333-33-3-333-333-3-333-3-3-11-113-300000000-33-33-11-11-11000000000000000000001-11-1-111-100000000
χ43333-33-3-3-3-33-33-33-3-333-11-113-3000000003-3-331-1-11-1100000000000000000000-11-111-11-100000000
χ44333-33-3-3-3-3-333-33-3-333-11-113-300000000-333-31-1-11-11000000000000000000001-11-11-1-1100000000
χ4566666660066-2-2000002-2-22-2-200000000-2-200002-2-220000000000000000000022-2-2000000000000
χ4666666660066-2-200000-222-2-2-200000000-2-20000-222-200000000000000000000-2-222000000000000
χ47666666600-6-6-2-2000002-2-22-2-2000000002200002-2-2200000000000000000000-2-222000000000000
χ48666666600-6-6-2-200000-222-2-2-200000000220000-222-20000000000000000000022-2-2000000000000
χ49666-66-6-6006-6-220000022-2-2-2200000000-22000022-2-2000000000000000000002-2-22000000000000
χ50666-66-6-6006-6-2200000-2-222-2200000000-220000-2-22200000000000000000000-222-2000000000000
χ51666-66-6-600-66-220000022-2-2-22000000002-2000022-2-200000000000000000000-222-2000000000000
χ52666-66-6-600-66-2200000-2-222-22000000002-20000-2-222000000000000000000002-2-22000000000000
χ5366-36-3-3-36600666-3-3-3-3-2-2-2-2-3-3000000000000-2-21111000000000000000000000000110000000000
χ5466-36-3-3-3-6-60066-63333-2-2-2-2-3-3000000000000221111000000000000000000000000-1-10000000000
χ5566-3-6-33366006-6-6-3-333-22-22-33000000000000-221-11-10000000000000000000000001-10000000000
χ5666-3-6-333-6-6006-6633-3-3-22-22-330000000000002-21-11-1000000000000000000000000-110000000000
χ578-880-8004-4000004-400000000222-22-2-2-20000000000222-22-2-2-20000000000000000000000000000
χ588-880-8004-4000004-400000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000000000000000
χ598-880-8004-4000004-400000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000000000000000
χ608-880-800-4400000-440000000022-22-22-2-2000000000022-22-22-2-20000000000000000000000000000
χ618-880-800-4400000-4400000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i30000000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i30000000000000000000000000000
χ628-880-800-4400000-4400000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i30000000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i30000000000000000000000000000
χ638-8-40443−434-400000-2223−23000000222-22-2-2-20000000000-1-1-11-111100003−33−33−33−30000000000000000
χ648-8-40443−434-400000-2223−23000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i3200002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ110000000000000000
χ658-8-40443−434-400000-2223−23000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ110000000000000000
χ668-8-40443−43-44000002-2−232300000022-22-22-2-20000000000-1-11-11-11100003−3−333−3−330000000000000000
χ678-8-40443−43-44000002-2−2323000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i3200002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ110000000000000000
χ688-8-40443−43-44000002-2−2323000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i320000−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ110000000000000000
χ698-8-404−43434-400000-22−2323000000222-22-2-2-20000000000-1-1-11-11110000−33−33−33−330000000000000000
χ708-8-404−43434-400000-22−2323000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i320000−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ110000000000000000
χ718-8-404−43434-400000-22−2323000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ110000000000000000
χ728-8-404−4343-44000002-223−2300000022-22-22-2-20000000000-1-11-11-1110000−333−3−333−30000000000000000
χ738-8-404−4343-44000002-223−23000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i320000−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ110000000000000000
χ748-8-404−4343-44000002-223−23000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i320000ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ110000000000000000
χ751212-612-6-6-60000-4-4000004-4-442200000000000000-222-2000000000000000000000000000000000000
χ761212-612-6-6-60000-4-400000-444-422000000000000002-2-22000000000000000000000000000000000000
χ771212-6-12-6660000-440000044-4-42-200000000000000-2-222000000000000000000000000000000000000
χ781212-6-12-6660000-4400000-4-4442-20000000000000022-2-2000000000000000000000000000000000000

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