Finite Group Databasebeta

← Group #130608

Character table — Group #130608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112244444444888888888888888161616161616161616161616161632323232
order12222222444444222444444444444444444444488888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-111-1-1-1-1-1-111-1-11-1-111111111-1-1-1-1
χ4111111111111111111-1-111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-11111-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-111-1-1
χ611111111111111-1-11111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-111
χ711111111111111-1-111-1-1-1-11111111-1-11-1-1-11111-1-1-1-1-1-111
χ811111111111111-1-111-1-1-1-11111111-1-11-1-1-1-1-1-1-1111111-1-1
χ91111111111-1-1-1-111-1111-1-111-1-1-1-1-1111-1-1-1ii−i−iii−i−ii−ii−i
χ101111111111-1-1-1-111-1111-1-111-1-1-1-1-1111-1-1-1−i−iii−i−iii−ii−ii
χ111111111111-1-1-1-111-11-1-1-1-1-1-11111-11-1-1-111ii−i−iii−i−i−ii−ii
χ121111111111-1-1-1-111-11-1-1-1-1-1-11111-11-1-1-111−i−iii−i−iiii−ii−i
χ131111111111-1-1-1-1-1-1-111111-1-11111-1-11-11-1-1ii−i−i−i−iiii−i−ii
χ141111111111-1-1-1-1-1-1-111111-1-11111-1-11-11-1-1−i−iiiii−i−i−iii−i
χ151111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−i
χ161111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii
χ1722222222-2-2222222-2-20022000000-2-200-200000000000000
χ1822222222-2-22222-2-2-2-200-2-2000000-2200200000000000000
χ1922222222-2-2-2-2-2-2222-200-2-20000002-200200000000000000
χ2022222222-2-2-2-2-2-2-2-22-200220000002200-200000000000000
χ21222222-2-22222-2-2002-200002222-2-2-200-2000000000000000
χ22222222-2-22222-2-2002-20000-2-2-2-222-2002000000000000000
χ23222222-2-222-2-22200-2-2000022-2-222200-2000000000000000
χ24222222-2-222-2-22200-2-20000-2-222-2-22002000000000000000
χ25222222-2-2-2-222-2-200-22220000000020-2002-2000000000000
χ26222222-2-2-2-222-2-200-22-2-20000000020200-22000000000000
χ27222222-2-2-2-2-2-22200222200000000-20-200-22000000000000
χ28222222-2-2-2-2-2-2220022-2-200000000-202002-2000000000000
χ2922-2-2-222-2002i−2i2i−2i2-200002i−2i00000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3022-2-2-222-2002i−2i2i−2i2-200002i−2i0000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3122-2-2-222-2002i−2i2i−2i-220000−2i2i00000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ3222-2-2-222-2002i−2i2i−2i-220000−2i2i0000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ3322-2-2-222-200−2i2i−2i2i2-20000−2i2i00000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ3422-2-2-222-200−2i2i−2i2i2-20000−2i2i0000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ3522-2-2-222-200−2i2i−2i2i-2200002i−2i00000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ3622-2-2-222-200−2i2i−2i2i-2200002i−2i0000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ374444-4-4004-400000000000000004i−4i0000000000000000000
χ384444-4-4004-40000000000000000−4i4i0000000000000000000
χ394444-4-400-44000000000000004i−4i000000000000000000000
χ404444-4-400-4400000000000000−4i4i000000000000000000000
χ4144-4-4-44-44004i−4i−4i4i000000000000000000000000000000000
χ4244-4-4-44-4400−4i4i4i−4i000000000000000000000000000000000
χ4388-8-88-800000000000000000000000000000000000000000
χ448-88-8000000000000004i−4i000000000000000000000000000
χ458-88-800000000000000−4i4i000000000000000000000000000
χ468-8-880000000000000000004-400000000000000000000000
χ478-8-88000000000000000000-4400000000000000000000000

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