Finite Group Databasebeta

← Group #135481

Character table — Group #135481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444888888888888888888888816163232323232323232
order12222222222222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ91111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-11-11-11-11-1
χ101111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-11-11-11-11
χ111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111i−ii−i−ii−ii
χ121111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111−ii−iii−ii−i
χ131111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111i−i−iii−i−ii
χ141111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−iii−i−iii−i
χ151111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-11-111-1
χ161111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-11-1-11
χ1722222222222222-2-2-2-2-2-2000000000000000022-2-2-2200000000
χ1822222222222222-2-2-2-2-2-20000000000000000-2-2222-200000000
χ192222222222-2-2-2-2-2-2-2-222000000000000000022-2-22-200000000
χ202222222222-2-2-2-2-2-2-2-2220000000000000000-2-222-2200000000
χ21222222-2-2-2-2000022-2-20000002i2i−2i−2i00002i2i−2i−2i2-22-20000000000
χ22222222-2-2-2-2000022-2-20000002i2i−2i−2i0000−2i−2i2i2i-22-220000000000
χ23222222-2-2-2-2000022-2-2000000−2i−2i2i2i00002i2i−2i−2i-22-220000000000
χ24222222-2-2-2-2000022-2-2000000−2i−2i2i2i0000−2i−2i2i2i2-22-20000000000
χ25222222-2-2-2-20000-2-222002i2i−2i−2i00002i2i−2i−2i00002-2-220000000000
χ26222222-2-2-2-20000-2-222002i2i−2i−2i0000−2i−2i2i2i0000-222-20000000000
χ27222222-2-2-2-20000-2-22200−2i−2i2i2i00002i2i−2i−2i0000-222-20000000000
χ28222222-2-2-2-20000-2-22200−2i−2i2i2i0000−2i−2i2i2i00002-2-220000000000
χ294444-4-44-4-4444-4-4000000000000000000000000000000000000
χ304444-4-44-4-44-4-444000000000000000000000000000000000000
χ314444-4-4-444-4000000004-4000000000000000000000000000000
χ324444-4-4-444-400000000-44000000000000000000000000000000
χ3344-4-400400-4004-40000002-22-22-22-20000000000000000000000
χ3444-4-400400-4004-4000000-22-22-22-220000000000000000000000
χ3544-4-400400-400-440000002-22-2-22-220000000000000000000000
χ3644-4-400400-400-44000000-22-222-22-20000000000000000000000
χ3744-4-400-40044-4000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ3844-4-400-40044-400000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ3944-4-400-4004-44000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4044-4-400-4004-4400000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ414-44-44-400000000004i−4i000000000000002+2i−2−2i2−2i−2+2i00000000000000
χ424-44-44-400000000004i−4i00000000000000−2−2i2+2i−2+2i2−2i00000000000000
χ434-44-44-40000000000−4i4i000000000000002−2i−2+2i2+2i−2−2i00000000000000
χ444-44-44-40000000000−4i4i00000000000000−2+2i2−2i−2−2i2+2i00000000000000
χ454-44-4-44000000004i−4i0000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ464-44-4-44000000004i−4i000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ474-44-4-4400000000−4i4i0000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ484-44-4-4400000000−4i4i000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ498-8-880008-800000000000000000000000000000000000000000
χ508-8-88000-8800000000000000000000000000000000000000000

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