Finite Group Databasebeta

← Group #67124

Character table — Group #67124

Order 360.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size112222222244444444444444444455101010101010101045454545
order1233336666510151515151515151530303030303030304412121212121212128888
χ1111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii
χ51-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109
χ61-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109
χ71-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119
χ81-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiiiζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119
χ9222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-10000
χ10222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2111-21110000
χ1122-12-1-1-12-1-122-1-122-1-1-1-1-1-122-1-1-1-122-12-1-1-12-1-10000
χ1222-12-1-1-12-1-122-1-122-1-1-1-1-1-122-1-1-1-1-2-21-2111-2110000
χ1322-1-12-1-1-12-122-1-1-1-122-1-1-1-1-1-122-1-122-1-12-1-1-12-10000
χ1422-1-12-1-1-12-122-1-1-1-122-1-1-1-1-1-122-1-1-2-211-2111-210000
χ1522-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-12-1-1-120000
χ1622-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-122-2-2111-2111-20000
χ172-22-1-1-1-21112-222-1-1-1-1-1-1-2-21111112i−2i2i−i−i−i−2iiii0000
χ182-22-1-1-1-21112-222-1-1-1-1-1-1-2-2111111−2i2i−2iiii2i−i−i−i0000
χ192-2-12-1-11-2112-2-1-122-1-1-1-111-2-211112i−2i−i2i−i−ii−2iii0000
χ202-2-12-1-11-2112-2-1-122-1-1-1-111-2-21111−2i2ii−2iii−i2i−i−i0000
χ212-2-1-12-111-212-2-1-1-1-122-1-11111-2-2112i−2i−i−i2i−iii−2ii0000
χ222-2-1-12-111-212-2-1-1-1-122-1-11111-2-211−2i2iii−2ii−i−i2i−i0000
χ232-2-1-1-12111-22-2-1-1-1-1-1-122111111-2-22i−2i−i−i−i2iiii−2i0000
χ242-2-1-1-12111-22-2-1-1-1-1-1-122111111-2-2−2i2iiii−2i−i−i−i2i0000
χ254444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ26444-2-2-24-2-2-2-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i15200000000000000
χ27444-2-2-24-2-2-2-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i15200000000000000
χ2844-24-2-2-24-2-2-1-11−i1521+i152-1-11−i1521+i1521+i1521−i1521−i1521+i152-1-11−i1521+i1521+i1521−i15200000000000000
χ2944-24-2-2-24-2-2-1-11+i1521−i152-1-11+i1521−i1521−i1521+i1521+i1521−i152-1-11+i1521−i1521−i1521+i15200000000000000
χ3044-2-24-2-2-24-2-1-11−i1521+i1521+i1521−i152-1-11−i1521+i1521−i1521+i1521+i1521−i152-1-11−i1521+i15200000000000000
χ3144-2-24-2-2-24-2-1-11+i1521−i1521−i1521+i152-1-11+i1521−i1521+i1521−i1521−i1521+i152-1-11+i1521−i15200000000000000
χ3244-2-2-24-2-2-24-1-11−i1521+i1521−i1521+i1521+i1521−i152-1-11−i1521+i1521−i1521+i1521+i1521−i152-1-100000000000000
χ3344-2-2-24-2-2-24-1-11+i1521−i1521+i1521−i1521−i1521+i152-1-11+i1521−i1521+i1521−i1521−i1521+i152-1-100000000000000
χ344-44444-4-4-4-4-11-1-1-1-1-1-1-1-11111111100000000000000
χ354-44-2-2-2-4222-11-1-11−i1521+i1521−i1521+i1521−i1521+i15211−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000
χ364-44-2-2-2-4222-11-1-11+i1521−i1521+i1521−i1521+i1521−i15211−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000
χ374-4-24-2-22-422-111−i1521+i152-1-11−i1521+i1521+i1521−i152−1+i152−1−i15211−1+i152−1−i152−1−i152−1+i15200000000000000
χ384-4-24-2-22-422-111+i1521−i152-1-11+i1521−i1521−i1521+i152−1−i152−1+i15211−1−i152−1+i152−1+i152−1−i15200000000000000
χ394-4-2-24-222-42-111−i1521+i1521+i1521−i152-1-11−i1521+i152−1+i152−1−i152−1−i152−1+i15211−1+i152−1−i15200000000000000
χ404-4-2-24-222-42-111+i1521−i1521−i1521+i152-1-11+i1521−i152−1−i152−1+i152−1+i152−1−i15211−1−i152−1+i15200000000000000
χ414-4-2-2-24222-4-111−i1521+i1521−i1521+i1521+i1521−i152-1-1−1+i152−1−i152−1+i152−1−i152−1−i152−1+i1521100000000000000
χ424-4-2-2-24222-4-111+i1521−i1521+i1521−i1521−i1521+i152-1-1−1−i152−1+i152−1−i152−1+i152−1+i152−1−i1521100000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.