Finite Group Databasebeta

← Group #13164598

Character table — Group #13164598

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444666666991212121212121212121212121212121212121212121212181818242424242424242424243636363648484848484854545454727272727272
order1222346661224449184433666121212181818181836363636363636363636244666699121218181212121218181818363622246612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i321−1−i32−1+i32111111111111111111111−1−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−i321−1+i32−1−i32111111111111111111111−1+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+i321−1−i32−1+i32111111111111111111-1-1-1−1−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−i321−1+i32−1−i32111111111111111111-1-1-1−1+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
χ7111-11-111-1-1-111-1111111-11111-11-1-1-1-1111111-1-1-1-1-11-11-11-111-1-11111111-11-1-1-111-1-1-1-11-11-1
χ8111-11-111-1-1-111-11111−1−i32−1+i32-1−1−i32−1+i3211-11-1-1-1-1111111-1-1-1-1-11-1−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i3211-1-11+i321−i32−1−i321+i32−1+i321−i32
χ9111-11-111-1-1-111-11111−1+i32−1−i32-1−1+i32−1−i3211-11-1-1-1-1111111-1-1-1-1-11-1−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i3211-1-11−i321+i32−1+i321−i32−1−i321+i32
χ10111-11-111-1-1-111-111-1-111-11111-11-1-1-1-1111111-1-1-1-11-111-11-111-1-111-1-1-1-11-11-1-1-1-1-11111-11-11
χ11111-11-111-1-1-111-111-1-1−1−i32−1+i32-1−1−i32−1+i3211-11-1-1-1-1111111-1-1-1-11-11−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i32-1-111−1−i32−1+i321+i32−1−i321−i32−1+i32
χ12111-11-111-1-1-111-111-1-1−1+i32−1−i32-1−1+i32−1−i3211-11-1-1-1-1111111-1-1-1-11-11−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i32-1-111−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-11-11-1-11-11111111-1111-11-11-1-1-1111-1-1-1111-1-1-11-11-1111-1-1111111-11-11-1-11-11-1-1-1-11-11
χ1411-111-11-11-1-11-111111−1−i32−1+i32-1−1−i32−1+i321-11-11-1-1-1111-1-1-1111-1-1-111+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i321-11-11+i321−i321+i32−1−i321−i32−1+i32
χ1511-111-11-11-1-11-111111−1+i32−1−i32-1−1+i32−1−i321-11-11-1-1-1111-1-1-1111-1-1-111−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i321-11-11−i321+i321−i32−1+i321+i32−1−i32
χ1611-111-11-11-1-11-1111-1-111-1111-11-11-1-1-1111-1-1-1111-111-1-11-1111-1-111-1-1-1-1-11-11-1-1-11-11111-11-1
χ1711-111-11-11-1-11-1111-1-1−1−i32−1+i32-1−1−i32−1+i321-11-11-1-1-1111-1-1-1111-111-11+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i32-11-11−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1811-111-11-11-1-11-1111-1-1−1+i32−1−i32-1−1+i32−1−i321-11-11-1-1-1111-1-1-1111-111-11−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i32-11-11−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-1111-1-1111-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111-1-1111-1-1-1-1
χ2011-1-1111-1-1111-1-11111−1−i32−1+i321−1−i32−1+i321-1-1-1-1111111-1-1-1-1-1-111-1-11+i321+i321−i321−i32−1−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+i321-1-11−1−i32−1+i321+i321+i321−i321−i32
χ2111-1-1111-1-1111-1-11111−1+i32−1−i321−1+i32−1−i321-1-1-1-1111111-1-1-1-1-1-111-1-11−i321−i321+i321+i32−1+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−i321-1-11−1+i32−1−i321−i321−i321+i321+i32
χ2211-1-1111-1-1111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-11-111-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-11111
χ2311-1-1111-1-1111-1-111-1-1−1−i32−1+i321−1−i32−1+i321-1-1-1-1111111-1-1-1-1-1-11-1111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2411-1-1111-1-1111-1-111-1-1−1+i32−1−i321−1+i32−1−i321-1-1-1-1111111-1-1-1-1-1-11-1111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222-1-10022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10002222-1-122-1-10000-1-1-1-1-1-10000000000
χ2622222222222222-1-100−1−i3−1+i32−1−i3−1+i3222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i31+i321−i3200001+i321+i321−i321−i321+i321−i320000000000
χ2722222222222222-1-100−1+i3−1−i32−1+i3−1−i3222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i31−i321+i3200001−i321−i321+i321+i321−i321+i320000000000
χ28222-22-222-2-2-222-2-1-10022-22222-2-11111-1-1-1-1-1-111110002-22-2-1-1-2-2-1-10000-11-11110000000000
χ29222-22-222-2-2-222-2-1-100−1−i3−1+i3-2−1−i3−1+i322-2-11111-1-1-1-1-1-11111000−1−i31+i3−1+i31−i31+i321−i321+i31−i31+i321−i3200001+i32−1−i321−i32−1+i32−1−i32−1+i320000000000
χ30222-22-222-2-2-222-2-1-100−1+i3−1−i3-2−1+i3−1−i322-2-11111-1-1-1-1-1-11111000−1+i31−i3−1−i31+i31−i321+i321−i31+i31−i321+i3200001−i32−1+i321+i32−1−i32−1+i32−1−i320000000000
χ3122-222-22-22-2-22-22-1-10022-2222-221-1111-1-1-1111-1-1-11000-22-22-1-1-2-2-1-100001-11-1110000000000
χ3222-222-22-22-2-22-22-1-100−1−i3−1+i3-2−1−i3−1+i32-221-1111-1-1-1111-1-1-110001+i3−1−i31−i3−1+i31+i321−i321+i31−i31+i321−i320000−1−i321+i32−1+i321−i32−1−i32−1+i320000000000
χ3322-222-22-22-2-22-22-1-100−1+i3−1−i3-2−1+i3−1−i32-221-1111-1-1-1111-1-1-110001−i3−1+i31+i3−1−i31−i321+i321−i31+i31−i321+i320000−1+i321−i32−1−i321+i32−1+i32−1−i320000000000
χ3422-2-2222-2-2222-2-2-1-100222222-2-211-1-1-1-1-1-1111111-1000-2-2-2-2-1-122-1-100001111-1-10000000000
χ3522-2-2222-2-2222-2-2-1-100−1−i3−1+i32−1−i3−1+i32-2-211-1-1-1-1-1-1111111-10001+i31+i31−i31−i31+i321−i32−1−i3−1+i31+i321−i320000−1−i32−1−i32−1+i32−1+i321+i321−i320000000000
χ3622-2-2222-2-2222-2-2-1-100−1+i3−1−i32−1+i3−1−i32-2-211-1-1-1-1-1-1111111-10001−i31−i31+i31+i31−i321+i32−1+i3−1−i31−i321+i320000−1+i32−1+i32−1−i32−1−i321−i321+i320000000000
χ373333333333-1-1-1-1333300-100-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-1000000
χ383333333333-1-1-1-133-3-300-100-1-1-133-1-1-1-1-1-1-1-1-1-1-1-13-3-3-3000000000000000000001111000000
χ39333-33-333-3-31-1-11333300100-1-113-3111-1-1-1-1-1-1111-3-33-300000000000000000000-1-111000000
χ40333-33-333-3-31-1-1133-3-300100-1-113-3111-1-1-1-1-1-1111-33-330000000000000000000011-1-1000000
χ4133-333-33-33-31-11-1333300100-11-1-33111-1-1-1111-1-1-1-3-3-3300000000000000000000-11-11000000
χ4233-333-33-33-31-11-133-3-300100-11-1-33111-1-1-1111-1-1-1-333-3000000000000000000001-11-1000000
χ4333-3-3333-3-33-1-111333300-100-111-3-3-1-1-1-1-1-111111133-3-300000000000000000000-111-1000000
χ4433-3-3333-3-33-1-11133-3-300-100-111-3-3-1-1-1-1-1-11111113-333000000000000000000001-1-11000000
χ454-40040-400000004-44i−4i-2-20220000000000000000000000000-2-200222i−2i2i−2i0000000000000000
χ464-40040-400000004-44i−4i1+i31−i30−1−i3−1+i300000000000000000000000001+i31−i300−1−i3−1+i3−2ζ152ζ15−2ζ32ζ30000000000000000
χ474-40040-400000004-44i−4i1−i31+i30−1+i3−1−i300000000000000000000000001−i31+i300−1+i3−1−i3−2ζ32ζ3−2ζ152ζ150000000000000000
χ484-40040-400000004-4−4i4i-2-20220000000000000000000000000-2-20022−2i2i−2i2i0000000000000000
χ494-40040-400000004-4−4i4i1+i31−i30−1−i3−1+i300000000000000000000000001+i31−i300−1−i3−1+i32ζ15−2ζ152ζ3−2ζ30000000000000000
χ504-40040-400000004-4−4i4i1−i31+i30−1+i3−1−i300000000000000000000000001−i31+i300−1+i3−1−i32ζ3−2ζ32ζ15−2ζ150000000000000000
χ516666666666-2-2-2-2-3-30000-200-2-2-2-3-3111111111111-3000000000000000000000000000000000
χ526666-36-3-3-3-36666000000-300-3-3-3000000000000000000000000000000000000000000000000
χ536666-36-3-3-3-3-2-2-2-2000000100111002ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ340000000000000000000000000000000000
χ546666-36-3-3-3-3-2-2-2-200000010011100−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ340000000000000000000000000000000000
χ556666-36-3-3-3-3-2-2-2-2000000100111002ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220000000000000000000000000000000000
χ56666-66-666-6-62-2-22-3-30000200-2-22-33-1-1-1111111-1-1-13000000000000000000000000000000000
χ57666-6-3-6-3-3332-2-22000000-10011-100−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340000000000000000000000000000000000
χ58666-6-3-6-3-3332-2-22000000-10011-100−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220000000000000000000000000000000000
χ59666-6-3-6-3-3332-2-22000000-10011-1002ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340000000000000000000000000000000000
χ60666-6-3-6-3-333-666-6000000300-3-33000000000000000000000000000000000000000000000000
χ6166-666-66-66-62-22-2-3-30000200-22-23-3-1-1-1111-1-1-11113000000000000000000000000000000000
χ6266-66-3-6-33-332-22-2000000-1001-1100−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ340000000000000000000000000000000000
χ6366-66-3-6-33-332-22-2000000-1001-1100−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220000000000000000000000000000000000
χ6466-66-3-6-33-332-22-2000000-1001-11002ζ14+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+2ζ340000000000000000000000000000000000
χ6566-66-3-6-33-33-66-66000000300-33-3000000000000000000000000000000000000000000000000
χ6666-6-6666-6-66-2-222-3-30000-200-22233111111-1-1-1-1-1-1-3000000000000000000000000000000000
χ6766-6-6-36-333-366-6-6000000-300-333000000000000000000000000000000000000000000000000
χ6866-6-6-36-333-3-2-2220000001001-1-1002ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340000000000000000000000000000000000
χ6966-6-6-36-333-3-2-2220000001001-1-100−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340000000000000000000000000000000000
χ7066-6-6-36-333-3-2-2220000001001-1-1002ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220000000000000000000000000000000000
χ718-80080-80000000-4400-4-404400000000000000000000000002200-2-200000000000000000000
χ728-80080-80000000-44002+2i32−2i30−2−2i3−2+2i30000000000000000000000000−1−i3−1+i3001+i31−i300000000000000000000
χ738-80080-80000000-44002−2i32+2i30−2+2i3−2−2i30000000000000000000000000−1+i3−1−i3001−i31+i300000000000000000000
χ7424-2400-120120000000000000000000000000000000000000000000000000000000000000000000

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