Finite Group Databasebeta

← Group #13164594

Character table — Group #13164594

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444666666991212121212121212121212121212121212121212121212181818242424242424242424243636363648484848484854545454727272727272
order1234446121212222491844336666612181818181818181818363636363636222991212121212121818121212123636363636362444666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i32111−1−i32−1+i321111111111111111111−1−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+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111111111111−1+i32−1−i32111−1+i32−1−i321111111111111111111−1+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−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ41111111111111111-1-111111111111111111111111-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1−1−i32−1+i32111−1−i32−1+i321111111111111111-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321−i321−i321−i32
χ61111111111111111-1-1−1+i32−1−i32111−1+i32−1−i321111111111111111-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321+i321+i321+i32
χ71111-1-111-1-11-1-111111111-1-1111111-1-1-1-1-1-11111-1-11-1-1111-1-11-1-11111111-1-11-1-111-1-11-1-11-1-1
χ81111-1-111-1-11-1-111111−1−i32−1+i321-1-1−1−i32−1+i321111-1-1-1-1-1-11111-1-11-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i321+i321+i32−1+i321−i321−i32
χ91111-1-111-1-11-1-111111−1+i32−1−i321-1-1−1+i32−1−i321111-1-1-1-1-1-11111-1-11-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i321−i321−i32−1−i321+i321+i32
χ101111-1-111-1-11-1-1111-1-1111-1-1111111-1-1-1-1-1-11111-1-1-111111-1-11-1-111-1-1-1-11-1-11-1-1-1-111-111-111
χ111111-1-111-1-11-1-1111-1-1−1−i32−1+i321-1-1−1−i32−1+i321111-1-1-1-1-1-11111-1-1-111−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32-1-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ121111-1-111-1-11-1-1111-1-1−1+i32−1−i321-1-1−1+i32−1−i321111-1-1-1-1-1-11111-1-1-111−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32-1-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ13111-11-11-11-1-11-11111111-11-1111-1-1-1111-1-1-1111-11-1-11-111-11-1-11-1111111-11-1-11-11-11-1-11-1-11-1
χ14111-11-11-11-1-11-111111−1−i32−1+i32-11-1−1−i32−1+i321-1-1-1111-1-1-1111-11-1-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321+i321−i32−1+i321−i321-11-11+i32−1−i321+i321−i32−1+i321−i32
χ15111-11-11-11-1-11-111111−1+i32−1−i32-11-1−1+i32−1−i321-1-1-1111-1-1-1111-11-1-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321−i321+i32−1−i321+i321-11-11−i32−1+i321−i321+i32−1−i321+i32
χ16111-11-11-11-1-11-1111-1-111-11-1111-1-1-1111-1-1-1111-11-11-1111-11-1-11-111-1-1-1-1-11-1-11-1-11-111-111-11
χ17111-11-11-11-1-11-1111-1-1−1−i32−1+i32-11-1−1−i32−1+i321-1-1-1111-1-1-1111-11-11-11−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321+i321−i32−1+i321−i32-11-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ18111-11-11-11-1-11-1111-1-1−1+i32−1−i32-11-1−1+i32−1−i321-1-1-1111-1-1-1111-11-11-11−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321−i321+i32−1−i321+i32-11-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ19111-1-111-1-11-1-111111111-1-11111-1-1-1-1-1-1111111-1-11-1-1111-1-11-1-11111111-1-11-1-111-1-11-1-11-1-11
χ20111-1-111-1-11-1-1111111−1−i32−1+i32-1-11−1−i32−1+i321-1-1-1-1-1-1111111-1-11-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-111+i321+i32−1−i321−i321−i32−1+i32
χ21111-1-111-1-11-1-1111111−1+i32−1−i32-1-11−1+i32−1−i321-1-1-1-1-1-1111111-1-11-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-111−i321−i32−1+i321+i321+i32−1−i32
χ22111-1-111-1-11-1-11111-1-111-1-11111-1-1-1-1-1-1111111-1-1111-111-1-11-1-1111-1-1-1-1-1-11-1-11-111-111-111-1
χ23111-1-111-1-11-1-11111-1-1−1−i32−1+i32-1-11−1−i32−1+i321-1-1-1-1-1-1111111-1-1111-1−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i32-111-1−1−i32−1−i321+i32−1+i32−1+i321−i32
χ24111-1-111-1-11-1-11111-1-1−1+i32−1−i32-1-11−1+i32−1−i321-1-1-1-1-1-1111111-1-1111-1−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i32-111-1−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2522222222222222-1-10022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-1-1222222-1-10000-1-1-1-1-1-10000000000
χ2622222222222222-1-100−1−i3−1+i3222−1−i3−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10001+i321−i32−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i321−i3200001+i321+i321+i321−i321−i321−i320000000000
χ2722222222222222-1-100−1+i3−1−i3222−1+i3−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10001−i321+i32−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i321+i3200001−i321−i321−i321+i321+i321+i320000000000
χ282222-2-222-2-22-2-22-1-100222-2-2222-1-1-1111111-1-1-1-111000-1-12-2-22-2-2-1-10000-111-1110000000000
χ292222-2-222-2-22-2-22-1-100−1−i3−1+i32-2-2−1−i3−1+i32-1-1-1111111-1-1-1-1110001+i321−i32−1−i31+i31+i3−1+i31−i31−i31+i321−i3200001+i32−1−i32−1−i321−i32−1+i32−1+i320000000000
χ302222-2-222-2-22-2-22-1-100−1+i3−1−i32-2-2−1+i3−1−i32-1-1-1111111-1-1-1-1110001−i321+i32−1+i31−i31−i3−1−i31+i31+i31−i321+i3200001−i32−1+i32−1+i321+i32−1−i32−1−i320000000000
χ31222-22-22-22-2-22-22-1-10022-22-2222111-1-1-1111-1-1-11-11000-1-1-22-2-22-2-1-100001-111-110000000000
χ32222-22-22-22-2-22-22-1-100−1−i3−1+i3-22-2−1−i3−1+i32111-1-1-1111-1-1-11-110001+i321−i321+i3−1−i31+i31−i3−1+i31−i31+i321−i320000−1−i321+i32−1−i32−1+i321−i32−1+i320000000000
χ33222-22-22-22-2-22-22-1-100−1+i3−1−i3-22-2−1+i3−1−i32111-1-1-1111-1-1-11-110001−i321+i321−i3−1+i31−i31+i3−1−i31+i31−i321+i320000−1+i321−i32−1+i32−1−i321+i32−1−i320000000000
χ34222-2-222-2-22-2-222-1-10022-2-22222111111-1-1-1-1-1-111-1000-1-1-2-22-2-22-1-1000011-111-10000000000
χ35222-2-222-2-22-2-222-1-100−1−i3−1+i3-2-22−1−i3−1+i32111111-1-1-1-1-1-111-10001+i321−i321+i31+i3−1−i31−i31−i3−1+i31+i321−i320000−1−i32−1−i321+i32−1+i32−1+i321−i320000000000
χ36222-2-222-2-22-2-222-1-100−1+i3−1−i3-2-22−1+i3−1−i32111111-1-1-1-1-1-111-10001−i321+i321−i31−i3−1+i31+i31+i3−1−i31−i321+i320000−1+i32−1+i321−i32−1−i32−1−i321+i320000000000
χ373333333333-1-1-1-1333300-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-133333300000000000000000000-1-1-1-1000000
χ383333333333-1-1-1-133-3-300-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1333-3-3-3000000000000000000001111000000
χ393333-3-333-3-3-111-1333300-11100-1-1-1-1111111-1-1-13-3-33-3-300000000000000000000-1-111000000
χ403333-3-333-3-3-111-133-3-300-11100-1-1-1-1111111-1-1-13-3-3-3330000000000000000000011-1-1000000
χ41333-33-33-33-31-11-13333001-1100-1111-1-1-1111-1-1-1-33-3-33-300000000000000000000-11-11000000
χ42333-33-33-33-31-11-133-3-3001-1100-1111-1-1-1111-1-1-1-33-33-33000000000000000000001-11-1000000
χ43333-3-333-3-3311-1-133330011-100-1111111-1-1-1-1-1-1-3-33-3-3300000000000000000000-111-1000000
χ44333-3-333-3-3311-1-133-3-30011-100-1111111-1-1-1-1-1-1-3-3333-3000000000000000000001-1-11000000
χ454-44000-400000004-44i−4i-2-2000220000000000000000000-2-2000000222i−2i2i−2i0000000000000000
χ464-44000-400000004-44i−4i1+i31−i3000−1−i3−1+i300000000000000000001+i31−i3000000−1−i3−1+i3−2ζ152ζ15−2ζ32ζ30000000000000000
χ474-44000-400000004-44i−4i1−i31+i3000−1+i3−1−i300000000000000000001−i31+i3000000−1+i3−1−i3−2ζ32ζ3−2ζ152ζ150000000000000000
χ484-44000-400000004-4−4i4i-2-2000220000000000000000000-2-200000022−2i2i−2i2i0000000000000000
χ494-44000-400000004-4−4i4i1+i31−i3000−1−i3−1+i300000000000000000001+i31−i3000000−1−i3−1+i32ζ15−2ζ152ζ3−2ζ30000000000000000
χ504-44000-400000004-4−4i4i1−i31+i3000−1+i3−1−i300000000000000000001−i31+i3000000−1+i3−1−i32ζ3−2ζ32ζ15−2ζ150000000000000000
χ516666666666-2-2-2-2-3-30000-2-2-200-2111111111111-3-3-3000000000000000000000000000000000
χ526666-6-666-6-6-222-2-3-30000-22200-2111-1-1-1-1-1-1111-333000000000000000000000000000000000
χ53666-66-66-66-62-22-2-3-300002-2200-2-1-1-1111-1-1-11113-33000000000000000000000000000000000
χ54666-6-666-6-6622-2-2-3-3000022-200-2-1-1-1-1-1-111111133-3000000000000000000000000000000000
χ5566-3666-3-3-3-36666000000-3-3-300-3000000000000000000000000000000000000000000000000
χ5666-3666-3-3-3-3-2-2-2-20000001110012ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000000000000000000000
χ5766-3666-3-3-3-3-2-2-2-2000000111001−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000000000000000000000
χ5866-3666-3-3-3-3-2-2-2-20000001110012ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000000000000000000000
χ5966-36-6-6-3-3336-6-66000000-33300-3000000000000000000000000000000000000000000000000
χ6066-36-6-6-3-333-222-20000001-1-10012ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000000000000000000000
χ6166-36-6-6-3-333-222-20000001-1-1001−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000000000000000000000
χ6266-36-6-6-3-333-222-20000001-1-10012ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000000000000000000000
χ6366-3-66-6-33-332-22-2000000-11-1001−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000000000000000000000
χ6466-3-66-6-33-332-22-2000000-11-1001−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000000000000000000000
χ6566-3-66-6-33-332-22-2000000-11-10012ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000000000000000000000
χ6666-3-66-6-33-33-66-660000003-3300-3000000000000000000000000000000000000000000000000
χ6766-3-6-66-333-322-2-2000000-1-11001−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000000000000000000000000000000000000
χ6866-3-6-66-333-322-2-2000000-1-11001−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000000000000000000000000000000000000
χ6966-3-6-66-333-322-2-2000000-1-110012ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000000000000000000000000000000000000
χ7066-3-6-66-333-3-6-66600000033-300-3000000000000000000000000000000000000000000000000
χ718-88000-80000000-4400-4-400044000000000000000000022000000-2-200000000000000000000
χ728-88000-80000000-44002+2i32−2i3000−2−2i3−2+2i30000000000000000000−1−i3−1+i30000001+i31−i300000000000000000000
χ738-88000-80000000-44002−2i32+2i3000−2+2i3−2−2i30000000000000000000−1+i3−1−i30000001−i31+i300000000000000000000
χ7424-24-12000120000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.