Finite Group Databasebeta

← Group #4094

Character table — Group #4094

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222222222224444444444445555101010101010
order1244222444551010202020201010101010102020202020208888888888
χ11111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111-1-11-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111-1-11-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111-11-1-11-111111111-1-111-1-1-1-111-1-11111-1-111-1-1
χ61111-11-1-11-111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-111
χ71111-1-11-1-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ81111-1-11-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ911-1-111-1-1-111111-1-1-1-11111-1-1-1-1-1-111ii−i−ii−ii−ii−i
χ1011-1-111-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−iii−ii−ii−ii
χ1111-1-11-11-11-11111-1-1-1-111-1-111-1-111-1-1ii−i−ii−i−ii−ii
χ1211-1-11-11-11-11111-1-1-1-111-1-111-1-111-1-1−i−iii−iii−ii−i
χ1311-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-1ii−i−i−iii−i−ii
χ1411-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-1−i−iiii−i−iii−i
χ1511-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111ii−i−i−ii−iii−i
χ1611-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111−i−iiii−ii−i−ii
χ172222222222−1+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
χ182222222222−1−52−1+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
χ1922222-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+520000000000
χ2022222-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−520000000000
χ212222-22-2-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+520000000000
χ222222-22-2-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1+521+521−520000000000
χ232222-2-22-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1−520000000000
χ242222-2-22-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1+520000000000
χ2522-2-222-2-2-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1−521−521+521−521+521−521+52−1+52−1−520000000000
χ2622-2-222-2-2-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1+521+521−521+521−521+521−52−1−52−1+520000000000
χ2722-2-22-22-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+520000000000
χ2822-2-22-22-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−520000000000
χ2922-2-2-2222-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ3022-2-2-2222-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ3122-2-2-2-2-2222−1+52−1−52−1+52−1−521−521−521+521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ3222-2-2-2-2-2222−1−52−1+52−1−52−1+521+521+521−521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ332-22i−2i00000022-2-22i−2i2i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ342-22i−2i00000022-2-22i−2i2i−2i0000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ352-2−2i2i00000022-2-2−2i2i−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ362-2−2i2i00000022-2-2−2i2i−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ374-44i−4i000000−1+5−1−51−51+5−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000
χ384-44i−4i000000−1−5−1+51+51−5−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000
χ394-4−4i4i000000−1+5−1−51−51+52ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000
χ404-4−4i4i000000−1−5−1+51+51−52ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000

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