Finite Group Databasebeta

← Group #65486

Character table — Group #65486

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222222224444444444444444448888888810101010202020202020
order1244245510102020202022448810102020404040404040404010101010202020208888448888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-11-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ4111111111111111-11-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111
χ511111111111111-11-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111
χ611111111111111-11-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ711111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ811111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ911-1-1-111111-1-1-1-111-1-11-1-1-1111111-1-1-1-11111-1-1-1-1ii−i−ii−ii−ii−i
χ1011-1-1-111111-1-1-1-111-1-11-1-1-1111111-1-1-1-11111-1-1-1-1−i−iii−ii−ii−ii
χ1111-1-1-111111-1-1-1-11-1-11-11-1-111-1-1-1-1111111-1-1-1-111ii−i−i−iii−i−ii
χ1211-1-1-111111-1-1-1-11-1-11-11-1-111-1-1-1-1111111-1-1-1-111−i−iiii−i−iii−i
χ1311-1-1-111111-1-1-1-1-111-1-11-1-111-1-1-1-11111-1-11111-1-1ii−i−i−ii−iii−i
χ1411-1-1-111111-1-1-1-1-111-1-11-1-111-1-1-1-11111-1-11111-1-1−i−iiii−ii−i−ii
χ1511-1-1-111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−ii−i−ii−ii
χ1611-1-1-111111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−iii−ii−i
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+52−1−52−1−522-22-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+520000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-22-22-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−521−521+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+522-22-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−520000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-22-22-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1+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
χ252222-2-222222222000000-2-2-2-200000000000000002-22-2000000
χ262222-2-222222222000000-2-2-2-20000000000000000-22-22000000
χ2722-2-22-22222-2-2-2-200000022-2-200000000000000002i−2i−2i2i000000
χ2822-2-22-22222-2-2-2-200000022-2-20000000000000000−2i2i2i−2i000000
χ2922-2-2-22−1+52−1−52−1+52−1−521−521−521+521+5222-2-22-21−521+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+520000000000
χ3022-2-2-22−1+52−1−52−1+52−1−521−521−521+521+522-2-22-221−521+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+52−1−520000000000
χ3122-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52-222-2-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521+520000000000
χ3222-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52-2-2222-21−521+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+52−1−520000000000
χ3322-2-2-22−1−52−1+52−1−52−1+521+521+521−521−5222-2-22-21+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+521−520000000000
χ3422-2-2-22−1−52−1+52−1−52−1+521+521+521−521−522-2-22-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+520000000000
χ3522-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52-222-2-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521−520000000000
χ3622-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52-2-2222-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
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
χ3944-4-44-4−1+5−1−5−1+5−1−51−51−51+51+5000000−1+5−1−51−51+500000000000000000000000000
χ4044-4-44-4−1−5−1+5−1−5−1+51+51+51−51−5000000−1−5−1+51+51−500000000000000000000000000
χ414-44i−4i0044-4-44i−4i4i−4i000000000000000000000000000000000000
χ424-44i−4i00−1+5−1−51−51+5−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000000
χ434-44i−4i00−1+5−1−51−51+5−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000000
χ444-44i−4i00−1−5−1+51+51−5−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000000
χ454-44i−4i00−1−5−1+51+51−5−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000000
χ464-4−4i4i0044-4-4−4i4i−4i4i000000000000000000000000000000000000
χ474-4−4i4i00−1+5−1−51−51+52ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000000
χ484-4−4i4i00−1+5−1−51−51+52ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000000
χ494-4−4i4i00−1−5−1+51+51−52ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000000
χ504-4−4i4i00−1−5−1+51+51−52ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000000

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