Finite Group Databasebeta

← Group #1219

Character table — Group #1219

Order 120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size1122222222222222151511222222222222221515
order1235561010151515153030303044226101061010303030303030303044
χ1111111111111111111111111111111111111
χ21111111111111111-1-11111111111111111-1-1
χ31-1111-1-1-11111-1-1-1-1i−i1-1111-1-1-11111-1-1-1-1i−i
χ41-1111-1-1-11111-1-1-1-1−ii1-1111-1-1-11111-1-1-1-1−ii
χ5222−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200222−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200
χ6222−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200222−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200
χ722-122-122-1-1-1-1-1-1-1-10022-122-122-1-1-1-1-1-1-1-100
χ822-1−1−52−1+52-1−1−52−1+52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ580022-1−1−52−1+52-1−1−52−1+52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ5800
χ922-1−1−52−1+52-1−1−52−1+52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ380022-1−1−52−1+52-1−1−52−1+52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ3800
χ1022-1−1+52−1−52-1−1+52−1−52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ340022-1−1+52−1−52-1−1+52−1−52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ3400
χ1122-1−1+52−1−52-1−1+52−1−52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ460022-1−1+52−1−52-1−1+52−1−52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ4600
χ122-22−1−52−1+52-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52002-22−1−52−1+52-21+521−52−1−52−1−52−1+52−1+521+521+521−521−5200
χ132-22−1+52−1−52-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52002-22−1+52−1−52-21−521+52−1+52−1+52−1−52−1−521−521−521+521+5200
χ142-2-1221-2-2-1-1-1-11111002-2-1221-2-2-1-1-1-1111100
χ152-2-1−1−52−1+5211+521−52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ58002-2-1−1−52−1+5211+521−52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ5800
χ162-2-1−1−52−1+5211+521−52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ38002-2-1−1−52−1+5211+521−52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ3800
χ172-2-1−1+52−1−5211−521+52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ34002-2-1−1+52−1−5211−521+52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ3400
χ182-2-1−1+52−1−5211−521+52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ46002-2-1−1+52−1−5211−521+52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ4600
χ19111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ211-1111-1-1-11111-1-1-1-1i−i-11-1-1-1111-1-1-1-11111−ii
χ221-1111-1-1-11111-1-1-1-1−ii-11-1-1-1111-1-1-1-11111i−i
χ23222−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200-2-2-21+521−52-21+521−521+521+521−521−521+521+521−521−5200
χ24222−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200-2-2-21−521+52-21−521+521−521−521+521+521−521−521+521+5200
χ2522-122-122-1-1-1-1-1-1-1-100-2-21-2-21-2-21111111100
χ2622-1−1−52−1+52-1−1−52−1+52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ5800-2-211+521−5211+521−52ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ58ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ5800
χ2722-1−1−52−1+52-1−1−52−1+52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ3800-2-211+521−5211+521−52ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ38ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ3800
χ2822-1−1+52−1−52-1−1+52−1−52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ3400-2-211−521+5211−521+52ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ34ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ3400
χ2922-1−1+52−1−52-1−1+52−1−52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ4600-2-211−521+5211−521+52ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ46ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ4600
χ302-22−1−52−1+52-21+521−52−1−52−1−52−1+52−1+521+521+521−521−5200-22-21+521−522−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200
χ312-22−1+52−1−52-21−521+52−1+52−1+52−1−52−1−521−521−521+521+5200-22-21−521+522−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200
χ322-2-1221-2-2-1-1-1-1111100-221-2-2-1221111-1-1-1-100
χ332-2-1−1−52−1+5211+521−52−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ58ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ5800-2211+521−52-1−1−52−1+52ζ26+ζ34ζ14+ζ46ζ22+ζ38ζ2+ζ58−ζ26−ζ34−ζ14−ζ46−ζ22−ζ38−ζ2−ζ5800
χ342-2-1−1−52−1+5211+521−52−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ38ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ3800-2211+521−52-1−1−52−1+52ζ14+ζ46ζ26+ζ34ζ2+ζ58ζ22+ζ38−ζ14−ζ46−ζ26−ζ34−ζ2−ζ58−ζ22−ζ3800
χ352-2-1−1+52−1−5211−521+52−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ34ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ3400-2211−521+52-1−1+52−1−52ζ22+ζ38ζ2+ζ58ζ14+ζ46ζ26+ζ34−ζ22−ζ38−ζ2−ζ58−ζ14−ζ46−ζ26−ζ3400
χ362-2-1−1+52−1−5211−521+52−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ46ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ4600-2211−521+52-1−1+52−1−52ζ2+ζ58ζ22+ζ38ζ26+ζ34ζ14+ζ46−ζ2−ζ58−ζ22−ζ38−ζ26−ζ34−ζ14−ζ4600

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.