Finite Group Databasebeta

← Group #4027

Character table — Group #4027

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222222222224444444444445555101010101010
order1222224444551010101010101010101020202020202020204444224444
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
χ51111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ61111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ71111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ91-11-11-1i−ii−i1111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1-11-1i−i
χ101-11-11-1i−ii−i1111-1-1-1-111-1-1ii−i−iii−i−i−i−iii-11-11−ii
χ111-11-11-1−ii−ii1111-1-1-1-111-1-1−i−iii−i−iiiii−i−i-11-11i−i
χ121-11-11-1−ii−ii1111-1-1-1-111-1-1−i−iii−i−iii−i−iii1-11-1−ii
χ131-11-1-11i−i−ii1111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i-111-1−ii
χ141-11-1-11i−i−ii1111-1-1-1-1-1-111ii−i−i−i−iii−i−iii1-1-11i−i
χ151-11-1-11−iii−i1111-1-1-1-1-1-111−i−iiiii−i−iii−i−i1-1-11−ii
χ161-11-1-11−iii−i1111-1-1-1-1-1-111−i−iiiii−i−i−i−iii-111-1i−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
χ2522-2-200000022-2-22-22-20000000000002i−2i2i−2i000000
χ2622-2-200000022-2-22-22-2000000000000−2i2i−2i2i000000
χ272-22-22-22i−2i2i−2i−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ282-22-22-22i−2i2i−2i−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ292-22-22-2−2i2i−2i2i−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ302-22-22-2−2i2i−2i2i−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ312-22-2-222i−2i−2i2i−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ322-22-2-222i−2i−2i2i−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ332-22-2-22−2i2i2i−2i−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ342-22-2-22−2i2i2i−2i−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ352-2-2200000022-2-2-22-220000000000002-2-22000000
χ362-2-2200000022-2-2-22-22000000000000-222-2000000
χ3744-4-4000000−1+5−1−51−51+5−1+51−5−1−51+50000000000000000000000
χ3844-4-4000000−1−5−1+51+51−5−1−51+5−1+51−50000000000000000000000
χ394-4-44000000−1+5−1−51−51+51−5−1+51+5−1−50000000000000000000000
χ404-4-44000000−1−5−1+51+51−51+5−1−51−5−1+50000000000000000000000

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