Finite Group Databasebeta

← Group #65046

Character table — Group #65046

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222224444444444444444448888888810101010202020202020
order1222445510101010101022448820202020404040404040404010101010202020204444444488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ41111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ511111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ611111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ91-11-1-1111-1-111-1-11-1i−ii−i11-1-1iiii−i−i−i−i11-1-1ii−i−ii−ii−i1-1i−i1-1
χ101-11-1-1111-1-111-1-11-1i−ii−i11-1-1iiii−i−i−i−i11-1-1ii−i−i−ii−ii-11−ii-11
χ111-11-1-1111-1-111-1-11-1−ii−ii11-1-1−i−i−i−iiiii11-1-1−i−iiii−ii−i-11i−i-11
χ121-11-1-1111-1-111-1-11-1−ii−ii11-1-1−i−i−i−iiiii11-1-1−i−iii−ii−ii1-1−ii1-1
χ131-11-1-1111-1-111-1-1-11i−i−ii11-1-1−i−i−i−iiiii-1-111ii−i−ii−ii−i1-1−ii-11
χ141-11-1-1111-1-111-1-1-11i−i−ii11-1-1−i−i−i−iiiii-1-111ii−i−i−ii−ii-11i−i1-1
χ151-11-1-1111-1-111-1-1-11−iii−i11-1-1iiii−i−i−i−i-1-111−i−iiii−ii−i-11−ii1-1
χ161-11-1-1111-1-111-1-1-11−iii−i11-1-1iiii−i−i−i−i-1-111−i−iii−ii−ii1-1i−i-11
χ17222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+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+52−1−520000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-222−1+52−1−52−1+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+520000000000
χ21222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1+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+520000000000
χ22222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-222−1−52−1+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+521−520000000000
χ252222-2-222222222000000-2-2-2-2000000000000000022-2-2000000
χ262222-2-222222222000000-2-2-2-20000000000000000-2-222000000
χ272-22-22-222-2-222-2-2000000-2-22200000000000000002i−2i−2i2i000000
χ282-22-22-222-2-222-2-2000000-2-2220000000000000000−2i2i2i−2i000000
χ292-22-2-22−1+52−1−521−521+52−1+52−1−521−521+522-22i−2i2i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−521−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ302-22-2-22−1+52−1−521−521+52−1+52−1−521−521+522-2−2i2i−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−1+52−1−521−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ312-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52-222i−2i−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ141−521+52−1+52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ322-22-2-22−1+52−1−521−521+52−1+52−1−521−521+52-22−2i2i2i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ141−521+52−1+52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ332-22-2-22−1−52−1+521+521−52−1−52−1+521+521−522-22i−2i2i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−1−52−1+521+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ342-22-2-22−1−52−1+521+521−52−1−52−1+521+521−522-2−2i2i−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−1−52−1+521+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ352-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52-222i−2i−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ381+521−52−1−52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ362-22-2-22−1−52−1+521+521−52−1−52−1+521+521−52-22−2i2i2i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ381+521−52−1−52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ374444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50000001−51+51−51+500000000000000000000000000
χ384444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50000001+51−51+51−500000000000000000000000000
χ3944-4-4004444-4-4-4-4000000000000000000000000000000000000
χ4044-4-400−1+5−1−5−1+5−1−51−51+51−51+50000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000000
χ4144-4-400−1+5−1−5−1+5−1−51−51+51−51+50000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000000
χ4244-4-400−1−5−1+5−1−5−1+51+51−51+51−50000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000000
χ4344-4-400−1−5−1+5−1−5−1+51+51−51+51−50000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000000
χ444-44-44-4−1+5−1−51−51+5−1+5−1−51−51+50000001−51+5−1+5−1−500000000000000000000000000
χ454-44-44-4−1−5−1+51+51−5−1−5−1+51+51−50000001+51−5−1−5−1+500000000000000000000000000
χ464-4-440044-4-4-4-444000000000000000000000000000000000000
χ474-4-4400−1+5−1−51−51+51−51+5−1+5−1−50000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ484-4-4400−1+5−1−51−51+51−51+5−1+5−1−50000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ494-4-4400−1−5−1+51+51−51+51−5−1−5−1+50000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000000
χ504-4-4400−1−5−1+51+51−51+51−5−1−5−1+50000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.