Finite Group Databasebeta

← Group #175309

Character table — Group #175309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444222444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-111-11-11-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111-1-111-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1111-1-111111111-1-1-1-1
χ911111111111-1-1-1-1-1-11111111-1-1-1-1-11111-1-11-1-11-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1-1-11111111-1-1-1-1-11-1-11-1-11-1-1111-1-111-1-111-1-111
χ1111111111111-1-1-1-1-1-111111-1-1-1-1-111-11111-1-111-1-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-1-1-111111-1-1-1-1-111-1-1-111-1-111-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1111-1-111-111-1-1-111-1-11111-1-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-1-1-1111-1-111-111-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1
χ1511111111111-1-1-1-1-1-1111-1-1-1-1-11111111-111-1-1-11-1-1-1-111-1-11111-1-1
χ1611111111111-1-1-1-1-1-1111-1-1-1-1-111111-1-1-111-1-1-111111-1-111-1-1-1-111
χ17222222222-2-222-2-2222-2-22200-2-2-200000-202000000000000000000
χ18222222222-2-222-2-2222-2-2-2-200-2220000020-2000000000000000000
χ19222222222-2-2-2-222-2-22-2-2220022200000-20-2000000000000000000
χ20222222222-2-2-2-222-2-22-2-2-2-2002-2-200000202000000000000000000
χ2122222222-22-22222-2-2-22-20022-200220000-20-200000000000000000
χ2222222222-22-22222-2-2-22-200-2-2-200-2-2000020200000000000000000
χ2322222222-22-2-2-2-2-222-22-20022200-2-2000020-200000000000000000
χ2422222222-22-2-2-2-2-222-22-200-2-2200220000-20200000000000000000
χ2522222222-2-2222-2-2-2-2-2-2200002000020000002-2-200000000000000
χ2622222222-2-2222-2-2-2-2-2-22000020000-2000000-22200000000000000
χ2722222222-2-22-2-22222-2-220000-200002000000-22-200000000000000
χ2822222222-2-22-2-22222-2-220000-20000-20000002-2200000000000000
χ29444-44-4-4-40004i−4i000000000000000002-200000002i−2i000000000000
χ30444-44-4-4-40004i−4i00000000000000000-220000000−2i2i000000000000
χ31444-44-4-4-4000−4i4i000000000000000002-20000000−2i2i000000000000
χ32444-44-4-4-4000−4i4i00000000000000000-2200000002i−2i000000000000
χ3344-44-44-4-400000004i−4i0000000000000000000000002-22i−2i00000000
χ3444-44-44-4-400000004i−4i000000000000000000000000-22−2i2i00000000
χ3544-44-44-4-40000000−4i4i0000000000000000000000002-2−2i2i00000000
χ3644-44-44-4-40000000−4i4i000000000000000000000000-222i−2i00000000
χ3744-4-4-4-444400000000-400000004i−4i00000000000000000000000000
χ3844-4-4-4-444400000000-40000000−4i4i00000000000000000000000000
χ3944-4-4-4-444-4000000004004-40000000000000000000000000000000
χ4044-4-4-4-444-400000000400-440000000000000000000000000000000
χ414-444-4-4-440400000000-4000000004i−4i000000000000000000000000
χ424-444-4-4-440400000000-400000000−4i4i000000000000000000000000
χ434-444-4-4-440-40000000040004-400000000000000000000000000000
χ444-444-4-4-440-4000000004000-4400000000000000000000000000000
χ454-4-444-44-400400000000-40000000000000000000000000002i2−2i20000
χ464-4-444-44-400400000000-4000000000000000000000000000−2i22i20000
χ474-4-444-44-400-4000000004000000000000000000000000022−22000000
χ484-4-444-44-400-40000000040000000000000000000000000−2222000000
χ494-4-4-444-44000004-400000000000000000000000000000000002-22-2
χ504-4-4-444-44000004-40000000000000000000000000000000000-22-22
χ514-4-4-444-4400000-4400000000000000000000000000000000002-2-22
χ524-4-4-444-4400000-440000000000000000000000000000000000-222-2
χ538-88-8-888-8000000000000000000000000000000000000000000000

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