Finite Group Databasebeta

← Group #257204

Character table — Group #257204

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111222244444488888888888161616161616161616161616161616161616161616161616
order12222222222244444422444444444244444444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-11-1-11-111-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-11-11-1-1-111-111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1111-1-111-11-11-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-11-1-1-1-1-1-11-1-1-11-1111111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-1-1-1-1-11-1-1-11-11-1-11-1-11111-1-1-1-11111
χ91111111111111-1-1111-1-111-111-1-111-1-1-1-1-111111-1-111-1-111-1-111-1-1
χ101111111111111-1-1111-1-111-111-1-111-1-1-1-1-111-1-1111-1-111-1-111-1-111
χ111111111111111-1-1111-1-111-1-1-1-1-1-1-111-1111-111-1-1-111-1-1-1-111-1-111
χ121111111111111-1-1111-1-111-1-1-1-1-1-1-111-1111-1-1-1-111-1-11111-1-111-1-1
χ131111111111111-1-1111-1-1-1-1-11111111-11-11-1-111-1-1-1-1-111-1-11111-1-1
χ141111111111111-1-1111-1-1-1-1-11111111-11-11-1-1-1-1-11111-1-111-1-1-1-111
χ151111111111111-1-1111-1-1-1-1-1-1-111-1-1-1111-1-11111-1-1-1-11111-1-1-1-111
χ161111111111111-1-1111-1-1-1-1-1-1-111-1-1-1111-1-11-1-111111-1-1-1-11111-1-1
χ17222222222222-222-2-2-2-2-222200220000-200-2000000000000000000
χ18222222222222-222-2-2-2-2-2-2-2200-2-200002002000000000000000000
χ19222222222222-2-2-2-2-2-22222-200-2-20000200-2000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-200220000-2002000000000000000000
χ2122222222-2-2-2-2222-2-222-200-22200-2-20-20200000000000000000000
χ2222222222-2-2-2-2222-2-222-200-2-2-20022020-200000000000000000000
χ2322222222-2-2-2-22-2-2-2-22-220022200-2-2020-200000000000000000000
χ2422222222-2-2-2-22-2-2-2-22-22002-2-200220-20200000000000000000000
χ2522222222-2-2-2-2-22222-2-2200-20000002000-20200-200000000000000
χ2622222222-2-2-2-2-22222-2-2200-2000000-200020-200200000000000000
χ2722222222-2-2-2-2-2-2-222-22-20020000002000-20-200200000000000000
χ2822222222-2-2-2-2-2-2-222-22-2002000000-200020200-200000000000000
χ2922-22-22-2-22-22-2-2002-22000002i−2i002i−2i00000000002i−2i00000000002-2
χ3022-22-22-2-22-22-2-2002-22000002i−2i002i−2i0000000000−2i2i0000000000-22
χ3122-22-22-2-22-22-2-2002-2200000−2i2i00−2i2i00000000002i−2i0000000000-22
χ3222-22-22-2-22-22-2-2002-2200000−2i2i00−2i2i0000000000−2i2i00000000002-2
χ3322-22-22-2-2-22-22-200-222000002i−2i00−2i2i00000002i−2i000000000002-200
χ3422-22-22-2-2-22-22-200-222000002i−2i00−2i2i0000000−2i2i00000000000-2200
χ3522-22-22-2-2-22-22-200-22200000−2i2i002i−2i00000002i−2i00000000000-2200
χ3622-22-22-2-2-22-22-200-22200000−2i2i002i−2i0000000−2i2i000000000002-200
χ3744-44-44-4-44-44-4400-44-400000000000000000000000000000000000
χ3844-44-44-4-4-44-444004-4-400000000000000000000000000000000000
χ3944-4-44-4-44000004i−4i000000000000000000000000002-22i−2i00000000
χ4044-4-44-4-44000004i−4i00000000000000000000000000-22−2i2i00000000
χ4144-4-44-4-4400000−4i4i000000000000000000000000002-2−2i2i00000000
χ4244-4-44-4-4400000−4i4i00000000000000000000000000-222i−2i00000000
χ434-4444-4-4-444-4-4000000004-40000000000000000000000000000000
χ444-4444-4-4-444-4-400000000-440000000000000000000000000000000
χ454-4444-4-4-4-4-44400000000000004i−4i00000000000000000000000000
χ464-4444-4-4-4-4-4440000000000000−4i4i00000000000000000000000000
χ474-4-44-4-4444-4-440000000000000000000000000000000000022−220000
χ484-4-44-4-4444-4-4400000000000000000000000000000000000−22220000
χ494-4-44-4-444-444-400000000000000000000000000000000022−22000000
χ504-4-44-4-444-444-4000000000000000000000000000000000−2222000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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