Finite Group Databasebeta

← Group #178189

Character table — Group #178189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444444444422444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111-11-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-11-1-11-11-111-1-1-111-111-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-11-1-11-11-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ71111111111111111111-1-11-1-1-11-1111-11-1-1-1111-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-11-1-1-11-11-1-1-11-1-1-11-1-111111111-1-1-1-1
χ911111111-1-11-1-111111-111-1-1-1111-111-111-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-111111-111-1-1-1111-1-1-1-111-1-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-111111-111-1-1-1-1-1-1111-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-11-1-111111-111-1-1-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1
χ1311111111-1-11-1-111111-1-1-1-1111-111111-1-1-1-11-1-1-1-11111-1-1-1-111
χ1411111111-1-11-1-111111-1-1-1-1111-111-1-11-1-1-1-111111-1-1-1-11111-1-1
χ1511111111-1-11-1-111111-1-1-1-111-11-1-11111-111-1-1-1-1-111-1-11111-1-1
χ1611111111-1-11-1-111111-1-1-1-111-11-1-1-1-111-111-11111-1-111-1-1-1-111
χ172222222222222-2-22-2-2-222-2-2-200000020-200000000000000000
χ182222222222222-2-22-2-2-2-2-2-222000000-20200000000000000000
χ192222222222-2-2-22-2-22-2200-200020-2000-2000200000000000000
χ202222222222-2-2-22-2-22-2200-2000-2020002000-200000000000000
χ212222222222-2-2-2-22-2-22-20020020-20000002-2000000000000000
χ222222222222-2-2-2-22-2-22-200200-202000000-22000000000000000
χ2322222222-2-22-2-2-2-22-2-2222222000000-20-200000000000000000
χ2422222222-2-22-2-2-2-22-2-22-2-22-2-200000020200000000000000000
χ2522222222-2-2-2222-2-22-2-2002000202000-2000-200000000000000
χ2622222222-2-2-2222-2-22-2-2002000-20-20002000200000000000000
χ2722222222-2-2-222-22-2-22200-20020-2000000-22000000000000000
χ2822222222-2-2-222-22-2-22200-200-2020000002-2000000000000000
χ29444-4-44-4-40040000-40004-400000000000000000000000000000
χ30444-4-44-4-40040000-4000-4400000000000000000000000000000
χ31444-4-44-4-400-4000040000004i−4i00000000000000000000000000
χ32444-4-44-4-400-400004000000−4i4i00000000000000000000000000
χ3344-444-4-4-400000400-4000000000000000000000000022−22000000
χ3444-444-4-4-400000400-40000000000000000000000000−2222000000
χ3544-444-4-4-400000-40040000000000000000000000000002i2−2i20000
χ3644-444-4-4-400000-4004000000000000000000000000000−2i22i20000
χ374-444-4-44-40004-40000000000000002i−2i0000002i−2i000000000000
χ384-444-4-44-40004-4000000000000000−2i2i000000−2i2i000000000000
χ394-444-4-44-4000-440000000000000002i−2i000000−2i2i000000000000
χ404-444-4-44-4000-44000000000000000−2i2i0000002i−2i000000000000
χ414-44-44-4-444-400000000000000000000000000002i−2i2i−2i00000000
χ424-44-44-4-444-40000000000000000000000000000−2i2i−2i2i00000000
χ434-44-44-4-44-4400000000000000000000000000002i−2i−2i2i00000000
χ444-44-44-4-44-440000000000000000000000000000−2i2i2i−2i00000000
χ454-4-4-4444-4000000400-40000000000000000000000000000002i2−2i2
χ464-4-4-4444-4000000400-4000000000000000000000000000000−2i22i2
χ474-4-4-4444-4000000-4004000000000000000000000000000022−2200
χ484-4-4-4444-4000000-40040000000000000000000000000000−222200
χ4988-8-8-8-888000000000000000000000000000000000000000000
χ508-8-88-88-88000000000000000000000000000000000000000000

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