Finite Group Databasebeta

← Group #299830

Character table — Group #299830

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222444444444488888888888881616161616161616161616161616161616163232
order12224444442444888888444488888888822444444888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-11111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-111-1-1111111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ911111111111111-1-1-1-1-1-111111111-1-1-1-1-11-11-11-11-111-1-1-1-111-1-11-1
χ1011111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11-11-11-1111-1-1-1-1-1-111-11
χ1111111111111111-1-1-1-1-1-11111-1-1-1-1-111111-11-11-11-1-1-1-1-111-1-111-11
χ1211111111111111-1-1-1-1-1-11111-1-1-1-1-11111-11-11-11-11-1-1-1-11111-1-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-11-1-11111-1-1111-1
χ1411111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1111111-1-1-11
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111111-1-111-1-1-11
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-11111-1-1-1-1111-1
χ172222222-2-22-2-22-222-2-22200000000-200002-200-2200000000000000
χ182222222-2-22-2-22-222-2-22200000000-20000-22002-200000000000000
χ192222222-2-22-2-22-2-2-222-2-200000000200002200-2-200000000000000
χ202222222-2-22-2-22-2-2-222-2-20000000020000-2-2002200000000000000
χ21222222-222-2-2-2-2200000022-2-222-2-200000000000002-20000000000
χ22222222-222-2-2-2-2200000022-2-2-2-2220000000000000-220000000000
χ23222222-222-2-2-2-22000000-2-22222-2-20000000000000-220000000000
χ24222222-222-2-2-2-22000000-2-222-2-22200000000000002-20000000000
χ252222-2-22222-22-2-222-2-2-2-20000000020000002-200-22000000000000
χ262222-2-22222-22-2-222-2-2-2-2000000002000000-22002-2000000000000
χ272222-2-22222-22-2-2-2-2222200000000-20000002200-2-2000000000000
χ282222-2-22222-22-2-2-2-2222200000000-2000000-2-20022000000000000
χ292222-2-22-2-222-2-222222-2-22-22-20000-2000000000000002-200000000
χ302222-2-22-2-222-2-222222-2-2-22-220000-200000000000000-2200000000
χ312222-2-22-2-222-2-22-2-2-2-2222-22-20000200000000000000-2200000000
χ322222-2-22-2-222-2-22-2-2-2-222-22-2200002000000000000002-200000000
χ332222-2-2-2-2-2-2-22220000002-2-220000022-2-20000000000002-2000000
χ342222-2-2-2-2-2-2-22220000002-2-2200000-2-222000000000000-22000000
χ352222-2-2-2-2-2-2-2222000000-222-20000022-2-2000000000000-22000000
χ362222-2-2-2-2-2-2-2222000000-222-200000-2-2220000000000002-2000000
χ37444444-4-4-4-444-4-4000000000000000000000000000000000000000
χ384444-4-4-444-44-44-4000000000000000000000000000000000000000
χ394-44-400-400400004i−4i00000000000000000000000000000002-22i−2i00
χ404-44-400-400400004i−4i0000000000000000000000000000000-22−2i2i00
χ414-44-400-40040000−4i4i00000000000000000000000000000002-2−2i2i00
χ424-44-400-40040000−4i4i0000000000000000000000000000000-222i−2i00
χ434-4-440004-4000000022−2222−220000002i2−2i202i−2i2i−2i00000000000000000000
χ444-4-440004-4000000022−2222−22000000−2i22i20−2i2i−2i2i00000000000000000000
χ454-4-440004-40000000−2222−22220000002i2−2i20−2i2i−2i2i00000000000000000000
χ464-4-440004-40000000−2222−2222000000−2i22i202i−2i2i−2i00000000000000000000
χ474-4-44000-44000000022−22−222200002i2−2i20002i−2i−2i2i00000000000000000000
χ484-4-44000-44000000022−22−22220000−2i22i2000−2i2i2i−2i00000000000000000000
χ494-4-44000-440000000−222222−2200002i2−2i2000−2i2i2i−2i00000000000000000000
χ504-4-44000-440000000−222222−220000−2i22i20002i−2i−2i2i00000000000000000000
χ5188-8-88-800000000000000000000000000000000000000000000000
χ5288-8-8-8800000000000000000000000000000000000000000000000
χ538-88-800800-80000000000000000000000000000000000000000000

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