Finite Group Databasebeta

← Group #4039

Character table — Group #4039

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222222222224444444444445555101010101010
order1222444444551010101010102020202020202020202020204444222244
χ11111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ4111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111-1-111-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ61111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ71111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ81111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ911-1-11-1i−ii−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i1-11-1i−i
χ1011-1-11-1i−ii−i11-1-111-1-111-1-1ii−i−iii−i−i−i−iii-11-11−ii
χ1111-1-11-1−ii−ii11-1-111-1-111-1-1−i−iii−i−iiiii−i−i-11-11i−i
χ1211-1-11-1−ii−ii11-1-111-1-111-1-1−i−iii−i−iii−i−iii1-11-1−ii
χ1311-1-1-11i−i−ii11-1-111-1-1-1-111ii−i−i−i−iiiii−i−i1-1-11−ii
χ1411-1-1-11i−i−ii11-1-111-1-1-1-111ii−i−i−i−iii−i−iii-111-1i−i
χ1511-1-1-11−iii−i11-1-111-1-1-1-111−i−iiiii−i−iii−i−i-111-1−ii
χ1611-1-1-11−iii−i11-1-111-1-1-1-111−i−iiiii−i−i−i−iii1-1-11i−i
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
χ19222222-2-2-2-2−1+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
χ20222222-2-2-2-2−1−52−1+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
χ212222-2-222-2-2−1+52−1−52−1+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
χ222222-2-222-2-2−1−52−1+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
χ232222-2-2-2-222−1+52−1−52−1+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
χ242222-2-2-2-222−1−52−1+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
χ2522-2-22-22i−2i2i−2i−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ2622-2-22-22i−2i2i−2i−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ2722-2-22-2−2i2i−2i2i−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ2822-2-22-2−2i2i−2i2i−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ2922-2-2-222i−2i−2i2i−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ3022-2-2-222i−2i−2i2i−1−52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ3122-2-2-22−2i2i2i−2i−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ3222-2-2-22−2i2i2i−2i−1−52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ332-22-20000002222-2-2-2-20000000000002i−2i2i−2i000000
χ342-22-20000002222-2-2-2-2000000000000−2i2i−2i2i000000
χ352-2-2200000022-2-2-2-2220000000000002-2-22000000
χ362-2-2200000022-2-2-2-222000000000000-222-2000000
χ374-44-4000000−1+5−1−5−1+5−1−51−51+51−51+50000000000000000000000
χ384-44-4000000−1−5−1+5−1−5−1+51+51−51+51−50000000000000000000000
χ394-4-44000000−1+5−1−51−51+51−51+5−1+5−1−50000000000000000000000
χ404-4-44000000−1−5−1+51+51−51+51−5−1−5−1+50000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.