Finite Group Databasebeta

← Group #10602744

Character table — Group #10602744

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55
size112222222224448888888888888888888888888888888888884040808080
order1225510101010101044422244410101010101010101010101020202020202020202020202020202020202024888
χ11111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1
χ3111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1
χ4111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111-11-1-11-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-1
χ611111111111111-11-1-11-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-11
χ711111111111111-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11
χ811111111111111-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1
χ9222222222222-2-200200-200000000222222-2-2-2-200000000-2-2-2-200000
χ10222222222222-2-200-200200000000-2-2-2-222-2-2-2-200000000222200000
χ1122222222222-22-20200-20000022220000-2-222-2-20000-2-2-2-2000000000
χ1222222222222-22-20-200200000-2-2-2-20000-2-222-2-200002222000000000
χ1322222222222-2-22200-200222200000000-2-2-2-222-2-2-2-20000000000000
χ1422222222222-2-22-200200-2-2-2-200000000-2-2-2-22222220000000000000
χ15222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000
χ16222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522222-2-22-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000
χ17222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-22-2-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000
χ18222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52222-2-22-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000
χ19222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-2-200200-2ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521−521+521+5200000
χ20222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-2-200200-2−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521−521+521+5200000
χ21222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-2-200-2002ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521−521+521+52−1+52−1−521−521+521−521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−1+52−1+52−1−52−1−5200000
χ22222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-2-200-2002−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521−521+521+52−1+52−1−521−521+521−521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−1+52−1+52−1−52−1−5200000
χ23222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-22-20200-20ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−1+52−1+52−1−52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521+52−1+52−1−521−521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521−521+521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ300000
χ24222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-22-20200-20−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−1+52−1+52−1−52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521+52−1+52−1−521−521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521−521+521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ300000
χ25222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-22-20-20020ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521−521+521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521+52−1+52−1−521−521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−1+52−1+52−1−52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ300000
χ26222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-22-20-20020−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521−521+521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521+52−1+52−1−521−521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−1+52−1+52−1−52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ300000
χ27222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22200-200−1+52−1+52−1−52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521+521−521+52−1+52−1−521−521−521+521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ300000
χ28222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22200-200−1+52−1+52−1−52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521+521−521+52−1+52−1−521−521−521+521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ300000
χ29222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22-2002001−521−521+521+52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ31−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ300000
χ30222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-22-2002001−521−521+521+52−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ31−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ300000
χ31222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000
χ32222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522222-2-22-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000
χ33222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-22-2-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000
χ34222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52222-2-22-2-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000
χ35222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-2-200200-2ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521+521−521−5200000
χ36222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-2-200200-2−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521+521−521−5200000
χ37222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-2-200-2002ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521+521−521−52−1−52−1+521+521−521+521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−1−52−1−52−1+52−1+5200000
χ38222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-2-200-2002−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521+521−521−52−1−52−1+521+521−521+521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−1−52−1−52−1+52−1+5200000
χ39222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-22-20200-20ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−1−52−1−52−1+52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521−52−1−52−1+521+521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521+521−521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ400000
χ40222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-22-20200-20−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−1−52−1−52−1+52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521−52−1−52−1+521+521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521+521−521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ400000
χ41222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-22-20-20020ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521+521−521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521−52−1−52−1+521+521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−1−52−1−52−1+52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ400000
χ42222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-22-20-20020−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521+521−521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521−52−1−52−1+521+521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−1−52−1−52−1+52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ400000
χ43222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22200-200−1−52−1−52−1+52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521−521+521−52−1−52−1+521+521+521−521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ400000
χ44222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22200-200−1−52−1−52−1+52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521−521+521−52−1−52−1+521+521+521−521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ400000
χ45222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22-2002001+521+521−521−52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ41+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ400000
χ46222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-22-2002001+521+521−521−52−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ4ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ41+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+52ζ2−ζ3−ζ2+ζ3−ζ+ζ4ζ−ζ4−ζ2+ζ3ζ2−ζ3ζ−ζ4−ζ+ζ400000
χ4744-4444-4-44-4-40000000000000000000000000000000000000002-2000
χ4844-4444-4-44-4-4000000000000000000000000000000000000000-22000
χ4988-8−2+25−2−25−2+252−252−25−2−252+252+2500000000000000000000000000000000000000000000
χ5088-8−2−25−2+25−2−252+252+25−2+252−252−2500000000000000000000000000000000000000000000
χ518-8088-800-80000000000000000000000000000000000000000000000
χ528-80−2+25−2−252−254ζ−4ζ4−4ζ+4ζ42+254ζ2−4ζ3−4ζ2+4ζ300000000000000000000000000000000000000000000
χ538-80−2+25−2−252−25−4ζ+4ζ44ζ−4ζ42+25−4ζ2+4ζ34ζ2−4ζ300000000000000000000000000000000000000000000
χ548-80−2−25−2+252+254ζ2−4ζ3−4ζ2+4ζ32−25−4ζ+4ζ44ζ−4ζ400000000000000000000000000000000000000000000
χ558-80−2−25−2+252+25−4ζ2+4ζ34ζ2−4ζ32−254ζ−4ζ4−4ζ+4ζ400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 5 (ζ5 = 1).