Finite Group Databasebeta

← Group #150484

Character table — Group #150484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size1122244448888888881616161616161616161616161616323232323232
order122442488224488888444448888888882416161616
χ111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1
χ41111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111-11-11-1-1-1-1-1ii−i−i11111ii−i−i-1-1ii−i−i
χ61111111111-11-11-1-1-1-1-1ii−i−i1-1-1-1-1ii−i−i11−i−iii
χ71111111111-11-11-1-1-1-1-1−i−iii11111−i−iii-1-1−i−iii
χ81111111111-11-11-1-1-1-1-1−i−iii1-1-1-1-1−i−iii11ii−i−i
χ91111111-1-1-11-11-1-1-111-11111111-1-1-1-1-1-11-11-11-1
χ101111111-1-1-11-11-1-1-111-111111-1-111-1-1-1-1-11-11-11
χ111111111-1-1-11-11-1-1-111-1-1-1-1-1111-1-111111-1-11-11
χ121111111-1-1-11-11-1-1-111-1-1-1-1-11-1-1111111-111-11-1
χ131111111-1-1-1-1-1-1-111-1-11ii−i−i111-1-1−i−iii-11i−i−ii
χ141111111-1-1-1-1-1-1-111-1-11ii−i−i1-1-111−i−iii1-1−iii−i
χ151111111-1-1-1-1-1-1-111-1-11−i−iii111-1-1ii−i−i-11−iii−i
χ161111111-1-1-1-1-1-1-111-1-11−i−iii1-1-111ii−i−i1-1i−i−ii
χ17222222222-22-22222-2-2-20000-200000000000000
χ18222222222-2-2-2-22-2-22220000-200000000000000
χ192222222-2-22222-2-2-2-2-220000-200000000000000
χ202222222-2-22-22-2-22222-20000-200000000000000
χ21222-2-22-20020-2002i−2i2i−2i01+i−1−i1−i−1+i000001+i−1−i1−i−1+i000000
χ22222-2-22-20020-2002i−2i2i−2i0−1−i1+i−1+i1−i00000−1−i1+i−1+i1−i000000
χ23222-2-22-20020-200−2i2i−2i2i01−i−1+i1+i−1−i000001−i−1+i1+i−1−i000000
χ24222-2-22-20020-200−2i2i−2i2i0−1+i1−i−1−i1+i00000−1+i1−i−1−i1+i000000
χ25222-2-22-200-202002i−2i−2i2i01−i−1+i1+i−1−i00000−1+i1−i−1−i1+i000000
χ26222-2-22-200-202002i−2i−2i2i0−1+i1−i−1−i1+i000001−i−1+i1+i−1−i000000
χ27222-2-22-200-20200−2i2i2i−2i01+i−1−i1−i−1+i00000−1−i1+i−1+i1−i000000
χ28222-2-22-200-20200−2i2i2i−2i0−1−i1+i−1+i1−i000001+i−1−i1−i−1+i000000
χ2944444-4-4440000-4000000000000000000000000
χ3044444-4-4-4-400004000000000000000000000000
χ31444-4-4-4400040-40000000000000000000000000
χ32444-4-4-44000-4040000000000000000000000000
χ3344-44-4004i−4i0000000000000002-22i−2i0000000000
χ3444-44-4004i−4i000000000000000-22−2i2i0000000000
χ3544-44-400−4i4i0000000000000002-2−2i2i0000000000
χ3644-44-400−4i4i000000000000000-222i−2i0000000000
χ3788-8-88000000000000000000000000000000000
χ3816-16000000000000000000000000000000000000

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