Finite Group Databasebeta

← Group #317993

Character table — Group #317993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order12224444442444888888888888888824444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111-1-11-1-1-1-11-11-11111-1-1-1-111-1-111-1-1
χ61111111111111111-1-1-1-1111-1-11-1-1-1-11-11-1-1-1-1-1111111-1-1-1-111
χ71111111111111111-1-1-1-1111-1-11-1-1-1-1-11-111111-1-1-1-1-1-111-1-111
χ81111111111111111-1-1-1-1111-1-11-1-1-1-1-11-11-1-1-1-11111-1-11111-1-1
χ911111111111111-1-11111-1-1-111-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11-1
χ1011111111111111-1-11111-1-1-111-1-1-1-1-11111-1-111-1-111-1-1-1-1-11-11
χ1111111111111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111-11-11
χ1211111111111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1-1-111-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-11-1-11
χ172222222-2-22-2-2-222222-2-2-2-2-22-2222-2-200000000000000000000
χ182222222-2-22-2-2-2222-2-222-2-2-2-222-2-22200000000000000000000
χ192222222-2-22-2-2-22-2-222-2-22222-2-2-2-22200000000000000000000
χ202222222-2-22-2-2-22-2-2-2-222222-22-222-2-200000000000000000000
χ2122222-2-2222-22-2-222000022-200-2000000002-22-2000000000000
χ2222222-2-2222-22-2-222000022-200-200000000-22-22000000000000
χ2322222-2-2222-22-2-2-2-20000-2-22002000000002-2-22000000000000
χ2422222-2-2222-22-2-2-2-20000-2-2200200000000-222-2000000000000
χ2522222-2-2-2-222-22-2220000-2-2200-20000000000002i−2i2i−2i00000000
χ2622222-2-2-2-222-22-2220000-2-2200-2000000000000−2i2i−2i2i00000000
χ2722222-2-2-2-222-22-2-2-2000022-20020000000000002i−2i−2i2i00000000
χ2822222-2-2-2-222-22-2-2-2000022-2002000000000000−2i2i2i−2i00000000
χ292222-22222-2-2-22-2002222000-2-20000022-2-20000000000000000
χ302222-22222-2-2-22-2002222000-2-200000-2-2220000000000000000
χ312222-22222-2-2-22-200-2-2-2-200022000002-2-220000000000000000
χ322222-22222-2-2-22-200-2-2-2-20002200000-222-20000000000000000
χ332222-222-2-2-222-2-20022-2-2000-22000000000000000002i−2i2i−2i0000
χ342222-222-2-2-222-2-20022-2-2000-2200000000000000000−2i2i−2i2i0000
χ352222-222-2-2-222-2-200-2-2220002-2000000000000000002i−2i−2i2i0000
χ362222-222-2-2-222-2-200-2-2220002-200000000000000000−2i2i2i−2i0000
χ374444-4-4-444-44-4-44000000000000000000000000000000000000
χ384444-4-4-4-4-4-4-4444000000000000000000000000000000000000
χ394-44-40004-4000002i2−2i22i2−2i22i2−2i22i2−2i200002-22-200000000000000000000
χ404-44-40004-4000002i2−2i2−2i22i2−2i22i22i2−2i20000-22-2200000000000000000000
χ414-44-40004-400000−2i22i22i2−2i22i2−2i2−2i22i20000-22-2200000000000000000000
χ424-44-40004-400000−2i22i2−2i22i2−2i22i2−2i22i200002-22-200000000000000000000
χ434-44-4000-44000002i2−2i22i2−2i2−2i22i2−2i22i200002-2-2200000000000000000000
χ444-44-4000-44000002i2−2i2−2i22i22i2−2i2−2i22i20000-222-200000000000000000000
χ454-44-4000-4400000−2i22i22i2−2i2−2i22i22i2−2i20000-222-200000000000000000000
χ464-44-4000-4400000−2i22i2−2i22i22i2−2i22i2−2i200002-2-2200000000000000000000
χ4788-8-808-80000000000000000000000000000000000000000000
χ4888-8-80-880000000000000000000000000000000000000000000
χ498-8-8880000-80000000000000000000000000000000000000000
χ508-8-88-8000080000000000000000000000000000000000000000

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