Finite Group Databasebeta

← Group #10613131

Character table — Group #10613131

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222222244444444444488888888888888888888888161616162020202020204040404040
order1222445510101010101024882020202020202020244481010202020202020202040404040404040401010202022448822248
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11
χ411111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1
χ51111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-11-1
χ61111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11
χ71111111111111111-1-111111111-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1
χ81111111111111111-1-111111111-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ911111111111111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-11-11-1
χ1011111111111111-1-111-1-1-1-111111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11-1-11-11-11
χ1111111111111111-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1111-11-1-1
χ1211111111111111-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11-1-1-11-111
χ1311111111111111-1-1-1-1-1-1-1-111111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-1-1-1111
χ1411111111111111-1-1-1-1-1-1-1-111111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-111111-1-1-1
χ1511111111111111-1-1-1-1-1-1-1-11111-11-111-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-111-1-11
χ1611111111111111-1-1-1-1-1-1-1-11111-11-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1111-1-111-1
χ17222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222222−1+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+52−1−5200000000000
χ18222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-22−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200000000000
χ19222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−5200000000000
χ20222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2−1+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+521−521+521−521+5200000000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2221−521−521+521+52−1+52−1+52−1−52−1−522-2-22-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+5200000000000
χ22222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2221−521−521+521+52−1+52−1+52−1−52−1−52-222-2-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−5200000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−522-22-221−521+521−521−521+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+5200000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52-22-2221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−5200000000000
χ25222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222222−1−52−1+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+5200000000000
χ26222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-22−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−5200000000000
χ27222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+5200000000000
χ28222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521−521+521−5200000000000
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2221+521+521−521−52−1−52−1−52−1+52−1+522-2-22-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−5200000000000
χ30222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2221+521+521−521−52−1−52−1−52−1+52−1+52-222-2-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+5200000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+522-22-221+521−521+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+521−5200000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52-22-2221+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+5200000000000
χ332222-2-2222222222-200-2-2-2-2-2-2-2-20000022000000000000000000002-2-220000000
χ342222-2-2222222222-200-2-2-2-2-2-2-2-2000002200000000000000000000-222-20000000
χ352222-2-222222222-22002222-2-2-2-200000-2-20000000000000000000022-2-20000000
χ362222-2-222222222-22002222-2-2-2-200000-2-200000000000000000000-2-2220000000
χ374444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-4001−51−51+51+51−51−51+51+500000−1+5−1−50000000000000000000000000000000
χ384444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4400−1+5−1+5−1−5−1−51−51−51+51+5000001−51+50000000000000000000000000000000
χ394444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-4001+51+51−51−51+51+51−51−500000−1−5−1+50000000000000000000000000000000
χ404444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4400−1−5−1−5−1+5−1+51+51+51−51−5000001+51−50000000000000000000000000000000
χ4144-4-40044-4-4-4-444000000000000000000000000000000000000000000022−2200000
χ4244-4-40044-4-4-4-4440000000000000000000000000000000000000000000−222200000
χ434-44-400444-44-4-4-40022−220000000000000000000000022−2222−220000000000000000000
χ444-44-400444-44-4-4-400−222200000000000000000000000−2222−22220000000000000000000
χ454-44-400−1+5−1−5−1+51−5−1−51+51−51+50022−22−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000
χ464-44-400−1+5−1−5−1+51−5−1−51+51−51+50022−222ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000−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+ζ39000000000000000
χ474-44-400−1+5−1−5−1+51−5−1−51+51−51+500−2222−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000
χ484-44-400−1+5−1−5−1+51−5−1−51+51−51+500−22222ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000ζ7−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−ζ39000000000000000
χ494-44-400−1−5−1+5−1−51+5−1+51−51+51−50022−222ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000ζ21+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+ζ37000000000000000
χ504-44-400−1−5−1+5−1−51+5−1+51−51+51−50022−22−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000ζ21+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−ζ37000000000000000
χ514-44-400−1−5−1+5−1−51+5−1+51−51+51−500−22222ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000−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−ζ37000000000000000
χ524-44-400−1−5−1+5−1−51+5−1+51−51+51−500−2222−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000−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+ζ37000000000000000
χ534-4-444-444-44-44-4-4000000004-44-400000000000000000000000000000000000000
χ544-4-444-4−1+5−1−51−5−1+51+5−1−51−51+500000000−1+51−5−1−51+500000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ554-4-444-4−1+5−1−51−5−1+51+5−1−51−51+500000000−1+51−5−1−51+5000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ564-4-444-4−1−5−1+51+5−1−51−5−1+51+51−500000000−1−51+5−1+51−5000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ574-4-444-4−1−5−1+51+5−1−51−5−1+51+51−500000000−1−51+5−1+51−500000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ584-4-44-4444-44-44-4-400000000-44-4400000000000000000000000000000000000000
χ594-4-44-44−1+5−1−51−5−1+51+5−1−51−51+5000000001−5−1+51+5−1−50000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ604-4-44-44−1+5−1−51−5−1+51+5−1−51−51+5000000001−5−1+51+5−1−500000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ614-4-44-44−1−5−1+51+5−1−51−5−1+51+51−5000000001+5−1−51−5−1+500000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ624-4-44-44−1−5−1+51+5−1−51−5−1+51+51−5000000001+5−1−51−5−1+50000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ6388-8-800−2+25−2−252−252−252+252+25−2+25−2−2500000000000000000000000000000000000000000000000000
χ6488-8-800−2−25−2+252+252+252−252−25−2−25−2+2500000000000000000000000000000000000000000000000000

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