Finite Group Databasebeta

← Group #132004

Character table — Group #132004

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244224444444224444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-111-1-1-1-11111-1-111-1-1-11-111111111-1-1-1-1
χ411111111111111111-1-111-1-1-1-11111-1-111-1-1-11-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11-111111-1-1-1-111-1-1
χ6111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11-11-1-1-1-11111-1-111
χ7111111111111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-111
χ8111111111111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1
χ911111111-1-11-11111-11111111111-1-111-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ1011111111-1-11-11111-11111111111-1-111-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ1111111111-1-11-11111-1-1-111-1-1-1-111-1-1-1-1-1-1111-11ii−i−iii−i−i−ii−ii
χ1211111111-1-11-11111-1-1-111-1-1-1-111-1-1-1-1-1-1111-11−i−iii−i−iiii−ii−i
χ1311111111-1-11-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-11-1ii−i−i−i−iiii−i−ii
χ1411111111-1-11-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-11-1−i−iiiii−i−i−iii−i
χ1511111111-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111ii−i−i−i−iii−iii−i
χ1611111111-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111−i−iiiii−i−ii−i−ii
χ172222222222222222200-2-20000-2-22200-2-2000-20000000000000
χ18222222222222-2-2-2-2200-2-2000022-2-200-2-200020000000000000
χ1922222222-2-22-22222-200-2-20000-2-2-2-2002200020000000000000
χ2022222222-2-22-2-2-2-2-2-200-2-2000022220022000-20000000000000
χ21222222-2-222-2-20000-2002-200220000-2-22-22-2000000000000000
χ22222222-2-222-2-20000-2002-200-2-20000222-2-22000000000000000
χ23222222-2-222-2-20000-222-22-2-200000000-220020-2000000000000
χ24222222-2-222-2-20000-2-2-2-222200000000-2200-202000000000000
χ25222222-2-2-2-2-2200002002-200220000-2-2-22-22000000000000000
χ26222222-2-2-2-2-2200002002-200-2-2000022-222-2000000000000000
χ27222222-2-2-2-2-220000222-22-2-2000000002-200-202000000000000
χ28222222-2-2-2-2-2200002-2-2-2222000000002-20020-2000000000000
χ294444-4-44400-4000000000000004i−4i00000000000000000000000
χ304444-4-44400-400000000000000−4i4i00000000000000000000000
χ314444-4-4-4-400404i4i−4i−4i0000000000000000000000000000000000
χ324444-4-4-4-40040−4i−4i4i4i0000000000000000000000000000000000
χ3344-4-4004i−4i00002+2i−2−2i2−2i−2+2i02-2002i−2i2i−2i00002-20000000000000000000
χ3444-4-4004i−4i00002+2i−2−2i2−2i−2+2i0-2200−2i2i−2i2i0000-220000000000000000000
χ3544-4-4004i−4i0000−2−2i2+2i−2+2i2−2i02-2002i−2i−2i2i0000-220000000000000000000
χ3644-4-4004i−4i0000−2−2i2+2i−2+2i2−2i0-2200−2i2i2i−2i00002-20000000000000000000
χ3744-4-400−4i4i00002−2i−2+2i2+2i−2−2i02-200−2i2i−2i2i00002-20000000000000000000
χ3844-4-400−4i4i00002−2i−2+2i2+2i−2−2i0-22002i−2i2i−2i0000-220000000000000000000
χ3944-4-400−4i4i0000−2+2i2−2i−2−2i2+2i02-200−2i2i2i−2i0000-220000000000000000000
χ4044-4-400−4i4i0000−2+2i2−2i−2−2i2+2i0-22002i−2i−2i2i00002-20000000000000000000
χ414-44-44-4004-4000000000000000000000000000000002-22-20000
χ424-44-44-4004-400000000000000000000000000000000-22-220000
χ434-44-44-400-44000000000000000000000000000000002i−2i−2i2i0000
χ444-44-44-400-4400000000000000000000000000000000−2i2i2i−2i0000
χ454-44-4-440000040000-40000000000000000000002i−2i2i−2i00000000
χ464-44-4-440000040000-4000000000000000000000−2i2i−2i2i00000000
χ474-44-4-4400000-4000040000000000000000000002-2-2200000000
χ484-44-4-4400000-400004000000000000000000000-222-200000000
χ498-8-88000000000000000000000004i−4i000000000000000000000
χ508-8-8800000000000000000000000−4i4i000000000000000000000

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