Finite Group Databasebeta

← Group #150556

Character table — Group #150556

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222244444444444444444448888888888888888444444888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ511111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-111111-1-1ii−i−i
χ611111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-1-111−i−iii
χ711111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-111111-1-1−i−iii
χ811111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-1-111ii−i−i
χ9111111-1-1-1-111111-1-11-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-111-11-1i−ii−i
χ10111111-1-1-1-111111-1-11-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-11-11−ii−ii
χ11111111-1-1-1-111111-1-11-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-111-11-1−ii−ii
χ12111111-1-1-1-111111-1-11-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-11-11i−ii−i
χ13111111-1-1-1-11-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-11-111-1-111-1-11
χ14111111-1-1-1-11-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-1
χ15111111-1-1-1-11-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-11-111-1-11-111-1
χ16111111-1-1-1-11-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-111-11-1-11
χ1722222222222222222222-2-22-2-20000000000000000-200-200000000
χ1822222222222-2-2-2-2-2-22-2-2-2-22220000000000000000200-200000000
χ19222222-2-2-2-222222-2-22-2-222-2220000000000000000-200-200000000
χ20222222-2-2-2-22-2-2-2-22222222-2-2-20000000000000000200-200000000
χ2122-2-22-20000-22i2i−2i−2i002002-202i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ2222-2-22-20000-22i2i−2i−2i002002-202i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ2322-2-22-20000-22i2i−2i−2i00200-220−2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ2422-2-22-20000-22i2i−2i−2i00200-220−2i2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ2522-2-22-20000-2−2i−2i2i2i002002-20−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
χ2622-2-22-20000-2−2i−2i2i2i002002-20−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000
χ2722-2-22-20000-2−2i−2i2i2i00200-2202i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ2822-2-22-20000-2−2i−2i2i2i00200-2202i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ294444444444-4000000-40000-4000000000000000000000000000000
χ30444444-4-4-4-4-4000000-400004000000000000000000000000000000
χ314444-4-444-4-400000000000000000000000000000000220-2-2000000
χ324444-4-444-4-400000000000000000000000000000000-2-2022000000
χ334444-4-4-4-444000000000000000000000000000000002-20-22000000
χ344444-4-4-4-44400000000000000000000000000000000-2202-2000000
χ3544-4-44-40000400004-4-44-4000000000000000000000000000000000
χ3644-4-44-4000040000-44-4-44000000000000000000000000000000000
χ374-44-4004-40002-22-2220-2-2000002−22−22−22−22−22−22−22−2000000000000
χ384-44-4004-40002-22-2220-2-200000−22−22−22−22−22−22−22−22000000000000
χ394-44-4004-4000-22-22-2-202200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ404-44-4004-4000-22-22-2-202200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ414-44-400-440002-22-2-2-202200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ424-44-400-440002-22-2-2-202200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ434-44-400-44000-22-22220-2-2000002−22−2−22−22−22−222−22−2000000000000
χ444-44-400-44000-22-22220-2-200000−22−222−22−22−22−2−22−22000000000000
χ454-4-4400004i−4i02i−2i−2i2i2-20-2200000i2−i2−i2i22−2−222−2−22−i2i2i2−i2000000000000
χ464-4-4400004i−4i02i−2i−2i2i2-20-2200000−i2i2i2−i2−222−2−222−2i2−i2−i2i2000000000000
χ474-4-4400004i−4i0−2i2i2i−2i-2202-2000002−2−22−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ484-4-4400004i−4i0−2i2i2i−2i-2202-200000−222−2i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ494-4-440000−4i4i02i−2i−2i2i-2202-2000002−2−22i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ504-4-440000−4i4i02i−2i−2i2i-2202-200000−222−2−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ514-4-440000−4i4i0−2i2i2i−2i2-20-2200000i2−i2−i2i2−222−2−222−2−i2i2i2−i2000000000000
χ524-4-440000−4i4i0−2i2i2i−2i2-20-2200000−i2i2i2−i22−2−222−2−22i2−i2−i2i2000000000000
χ5388-8-8-8800000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).