Finite Group Databasebeta

← Group #4033

Character table — Group #4033

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222222222224444444444445555101010101010
order1222444444551010101010102020202020202020202020204444444444
χ11111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ4111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ51111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ61111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ81111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ91-1-11i−ii−i1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−ii−i1-11-1
χ101-1-11i−ii−i1-111-1-111-1-111-1-1ii−i−iii−i−i−i−iii−ii-11-11
χ111-1-11i−i−ii-1111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−ii1-1-11
χ121-1-11i−i−ii-1111-1-111-1-1-1-111ii−i−i−i−iii−i−iiii−i-111-1
χ131-1-11−iii−i-1111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−ii-111-1
χ141-1-11−iii−i-1111-1-111-1-1-1-111−i−iiiii−i−i−i−iiii−i1-1-11
χ151-1-11−ii−ii1-111-1-111-1-111-1-1−i−iii−i−iiiii−i−ii−i-11-11
χ161-1-11−ii−ii1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−ii1-11-1
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+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ20222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+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+521−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ222222-2-222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ232222-2-2-2-222−1+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
χ242222-2-2-2-222−1−52−1+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
χ2522-2-20000002222-2-2-2-20000000000002-22-2000000
χ2622-2-20000002222-2-2-2-2000000000000-22-22000000
χ272-22-200000022-2-2-2-2220000000000002i−2i−2i2i000000
χ282-22-200000022-2-2-2-222000000000000−2i2i2i−2i000000
χ292-2-222i−2i2i−2i2-2−1+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
χ302-2-222i−2i2i−2i2-2−1−52−1+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
χ312-2-222i−2i−2i2i-22−1+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
χ322-2-222i−2i−2i2i-22−1−52−1+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
χ332-2-22−2i2i2i−2i-22−1+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
χ342-2-22−2i2i2i−2i-22−1−52−1+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
χ352-2-22−2i2i−2i2i2-2−1+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
χ362-2-22−2i2i−2i2i2-2−1−52−1+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
χ3744-4-4000000−1+5−1−5−1+5−1−51−51+51−51+50000000000000000000000
χ3844-4-4000000−1−5−1+5−1−5−1+51+51−51+51−50000000000000000000000
χ394-44-4000000−1+5−1−51−51+51−51+5−1+5−1−50000000000000000000000
χ404-44-4000000−1−5−1+51+51−51+51−5−1−5−1+50000000000000000000000

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