Finite Group Databasebeta

← Group #301994

Character table — Group #301994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222444444444488888888888881616161616161616161616161616161616163232
order12222222442444888888244444448888822444444444444888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ511111111111111111111-1-1-1-11111111111-11-11-1111-111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111111-11-11-11-1-1-11-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-11-11-1-1-11-1-1-111-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-11-1111-111111-1-111-1-1
χ911111111111111-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-1-111-1-1-1-1111-1
χ1011111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-111-11
χ1111111111111111-1-1-1-1-1-11111-1-1-1-1-1111111-111-111-1-1-1-111-1-1-1-1-11
χ1211111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1-11-1-1111111-1-1-1-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-111-1-1-11111111-1-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1111-1-1-11111-1-11-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-11-1-1-1-111111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11-111-1-11111-11
χ17222222-2-222-22-2-22222-2-200000000-200002020-2000-200000000000
χ18222222-2-222-22-2-22222-2-200000000-20000-20-202000200000000000
χ19222222-2-222-22-2-2-2-2-2-222000000002000020-20-2000200000000000
χ20222222-2-222-22-2-2-2-2-2-2220000000020000-20202000-200000000000
χ21222222-2-2-2-2-2-22200000022-2-222-2-20000000000000000000002-200
χ22222222-2-2-2-2-2-22200000022-2-2-2-222000000000000000000000-2200
χ23222222-2-2-2-2-2-222000000-2-22222-2-2000000000000000000000-2200
χ24222222-2-2-2-2-2-222000000-2-222-2-2220000000000000000000002-200
χ252222-2-22222-2-22-222-2-22200000000-20000020-20-200020000000000
χ262222-2-22222-2-22-222-2-22200000000-200000-20202000-20000000000
χ272222-2-22222-2-22-2-2-222-2-20000000020000020-202000-20000000000
χ282222-2-22222-2-22-2-2-222-2-200000000200000-2020-200020000000000
χ292222-2-222-2-2-22-220000002-22-20000022-2-20000000000002-2000000
χ302222-2-222-2-2-22-220000002-22-200000-2-222000000000000-22000000
χ312222-2-222-2-2-22-22000000-22-220000022-2-2000000000000-22000000
χ322222-2-222-2-2-22-22000000-22-2200000-2-2220000000000002-2000000
χ332222-2-2-2-2222-2-2222-2-2-2-22-2-22000020000000000000000002-20000
χ342222-2-2-2-2222-2-2222-2-2-2-2-222-200002000000000000000000-220000
χ352222-2-2-2-2222-2-22-2-222222-2-220000-2000000000000000000-220000
χ362222-2-2-2-2222-2-22-2-22222-222-20000-20000000000000000002-20000
χ3744444444-4-44-4-4-4000000000000000000000000000000000000000
χ384444-4-4-4-4-4-4444-4000000000000000000000000000000000000000
χ394-44-4004-40000002i2−2i2002i2−2i200002i−2i2i−2i00022−2200000000000000000000
χ404-44-4004-40000002i2−2i2002i2−2i20000−2i2i−2i2i000−222200000000000000000000
χ414-44-4004-4000000−2i22i200−2i22i200002i−2i2i−2i000−222200000000000000000000
χ424-44-4004-4000000−2i22i200−2i22i20000−2i2i−2i2i00022−2200000000000000000000
χ434-44-400-440000002i2−2i200−2i22i200002i−2i−2i2i022−220000000000000000000000
χ444-44-400-440000002i2−2i200−2i22i20000−2i2i2i−2i0−22220000000000000000000000
χ454-44-400-44000000−2i22i2002i2−2i200002i−2i−2i2i0−22220000000000000000000000
χ464-44-400-44000000−2i22i2002i2−2i20000−2i2i2i−2i022−220000000000000000000000
χ474-4-4400004-40000004i−4i0000000000000000000002i−2i002-200000000
χ484-4-4400004-40000004i−4i000000000000000000000−2i2i00-2200000000
χ494-4-4400004-4000000−4i4i0000000000000000000002i−2i00-2200000000
χ504-4-4400004-4000000−4i4i000000000000000000000−2i2i002-200000000
χ5188-8-88-800000000000000000000000000000000000000000000000
χ5288-8-8-8800000000000000000000000000000000000000000000000
χ538-8-880000-880000000000000000000000000000000000000000000

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