Finite Group Databasebeta

← Group #11757435

Character table — Group #11757435

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size1113333399999999992727272727272727363636363636108108108108
order133233666699181818181818336666669999993399
χ1111111111111111111111111111111111111
χ211111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ311111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1−i32−1+i32
χ5111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3211
χ6111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1+i32−1−i32
χ7111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1+i32−1−i32
χ8111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1−i32−1+i32
χ9111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3211
χ103333333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000000000000000
χ113333333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000000000000000
χ123333−3+3i32−3−3i3233−3+3i32−3−3i320000000000000000ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ50000
χ133333−3+3i32−3−3i3233−3+3i32−3−3i320000000000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ50000
χ143333−3+3i32−3−3i3233−3+3i32−3−3i320000000000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ50000
χ153333−3−3i32−3+3i3233−3−3i32−3+3i3200000000000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40000
χ163333−3−3i32−3+3i3233−3−3i32−3+3i320000000000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40000
χ173333−3−3i32−3+3i3233−3−3i32−3+3i320000000000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40000
χ18333-133-1-1-1-133-1-1-1-1-1-133-1-1-1-1-1-10000000000
χ19333-133-1-1-1-133-1-1-1-1-1-1−3+3i32−3−3i321−i321−i321−i321+i321+i321+i320000000000
χ20333-133-1-1-1-133-1-1-1-1-1-1−3−3i32−3+3i321+i321+i321+i321−i321−i321−i320000000000
χ21333-133-1-1-1-1−3+3i32−3−3i321−i321−i321−i321+i321+i321+i32002−1+i3−1−i32−1+i3−1−i30000000000
χ22333-133-1-1-1-1−3+3i32−3−3i321−i321−i321−i321+i321+i321+i3200−1+i3−1−i32−1−i32−1+i30000000000
χ23333-133-1-1-1-1−3+3i32−3−3i321−i321−i321−i321+i321+i321+i3200−1−i32−1+i3−1+i3−1−i320000000000
χ24333-133-1-1-1-1−3−3i32−3+3i321+i321+i321+i321−i321−i321−i32002−1−i3−1+i32−1−i3−1+i30000000000
χ25333-133-1-1-1-1−3−3i32−3+3i321+i321+i321+i321−i321−i321−i3200−1+i32−1−i3−1−i3−1+i320000000000
χ26333-133-1-1-1-1−3−3i32−3+3i321+i321+i321+i321−i321−i321−i3200−1−i3−1+i32−1+i32−1−i30000000000
χ27999-3−9+9i32−9−9i32-3-33−3i323+3i3200000000000000000000000000
χ28999-3−9−9i32−9+9i32-3-33+3i323−3i3200000000000000000000000000
χ299−9+9i32−9−9i32900−9+9i32−9−9i320000000000000000000000000000
χ309−9+9i32−9−9i32-3003−3i323+3i3200002ζ+4ζ42ζ−2ζ4−4ζ−2ζ44ζ2+2ζ5−2ζ2+2ζ5−2ζ2−4ζ5000000000000000000
χ319−9+9i32−9−9i32-3003−3i323+3i3200002ζ−2ζ4−4ζ−2ζ42ζ+4ζ4−2ζ2+2ζ5−2ζ2−4ζ54ζ2+2ζ5000000000000000000
χ329−9+9i32−9−9i32-3003−3i323+3i320000−4ζ−2ζ42ζ+4ζ42ζ−2ζ4−2ζ2−4ζ54ζ2+2ζ5−2ζ2+2ζ5000000000000000000
χ339−9−9i32−9+9i32900−9−9i32−9+9i320000000000000000000000000000
χ349−9−9i32−9+9i32-3003+3i323−3i3200004ζ2+2ζ5−2ζ2+2ζ5−2ζ2−4ζ52ζ−2ζ4−4ζ−2ζ42ζ+4ζ4000000000000000000
χ359−9−9i32−9+9i32-3003+3i323−3i320000−2ζ2+2ζ5−2ζ2−4ζ54ζ2+2ζ5−4ζ−2ζ42ζ+4ζ42ζ−2ζ4000000000000000000
χ369−9−9i32−9+9i32-3003+3i323−3i320000−2ζ2−4ζ54ζ2+2ζ5−2ζ2+2ζ52ζ+4ζ42ζ−2ζ4−4ζ−2ζ4000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.