Finite Group Databasebeta

← Group #65178

Character table — Group #65178

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222224444444444444444448888888810101010202020202020
order1222445510101010101044448820202020404040404040404020202020202020204444224488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ41111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ611111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
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
χ91-1-111-111-1-111-1-1i−ii−i1-1-1-1111111-1-1-1-1ii−i−iii−i−ii−ii−i1-11-1i−i
χ101-1-111-111-1-111-1-1i−ii−i1-1-1-1111111-1-1-1-1ii−i−iii−i−i−ii−ii-11-11−ii
χ111-1-111-111-1-111-1-1i−i−ii-11-1-111-1-1-1-11111ii−i−i−i−iiii−ii−i1-1-11−ii
χ121-1-111-111-1-111-1-1i−i−ii-11-1-111-1-1-1-11111ii−i−i−i−iii−ii−ii-111-1i−i
χ131-1-111-111-1-111-1-1−iii−i-11-1-111-1-1-1-11111−i−iiiii−i−ii−ii−i-111-1−ii
χ141-1-111-111-1-111-1-1−iii−i-11-1-111-1-1-1-11111−i−iiiii−i−i−ii−ii1-1-11i−i
χ151-1-111-111-1-111-1-1−ii−ii1-1-1-1111111-1-1-1-1−i−iii−i−iiii−ii−i-11-11i−i
χ161-1-111-111-1-111-1-1−ii−ii1-1-1-1111111-1-1-1-1−i−iii−i−iii−ii−ii1-11-1−ii
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
χ272-2-222-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i2i−2i2-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ282-2-222-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−2i2i-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ292-2-222-2−1+52−1−521−521+52−1+52−1−521−521+52−2i2i2i−2i-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ302-2-222-2−1+52−1−521−521+52−1+52−1−521−521+52−2i2i−2i2i2-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ312-2-222-2−1−52−1+521+521−52−1−52−1+521+521−522i−2i2i−2i2-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ322-2-222-2−1−52−1+521+521−52−1−52−1+521+521−522i−2i−2i2i-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ332-2-222-2−1−52−1+521+521−52−1−52−1+521+521−52−2i2i2i−2i-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ342-2-222-2−1−52−1+521+521−52−1−52−1+521+521−52−2i2i−2i2i2-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ352-2-22-2222-2-222-2-200000022-2-200000000000000002i−2i−2i2i000000
χ362-2-22-2222-2-222-2-200000022-2-20000000000000000−2i2i2i−2i000000
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+50000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ4144-4-400−1+5−1−5−1+5−1−51−51+51−51+50000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−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+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000000
χ4344-4-400−1−5−1+5−1−5−1+51+51−51+51−50000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000000
χ444-44-40044-4-4-4-444000000000000000000000000000000000000
χ454-44-400−1+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
χ464-44-400−1+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
χ474-44-400−1−5−1+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
χ484-44-400−1−5−1+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
χ494-4-44-44−1+5−1−51−51+5−1+5−1−51−51+5000000−1+5−1−51−51+500000000000000000000000000
χ504-4-44-44−1−5−1+51+51−5−1−5−1+51+51−5000000−1−5−1+51+51−500000000000000000000000000

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