Finite Group Databasebeta

← Group #256542

Character table — Group #256542

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444244444888888884444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111-1-11111-1-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-11-1-11111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-11-1-111111111-1-11-1-1-1-1-1-111-1-11-1-1-1-11111
χ7111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-11111
χ8111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111111-1-1-1-1
χ911111111-1-1-1-1-1-1111111-111-1111111-1-1-1-11-11-1-1111-11-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1111111-111-1111111-1-1-1-1-11-1-1-111-11-11-1-11-1-111-1-111
χ1111111111-1-1-1-1-1-1111111-111-111-1-1-1-111111-11-1-1-1-11-11-111-1-1-111-1-111
χ1211111111-1-1-1-1-1-1111111-111-111-1-1-1-11111-11-1-1-1-1-1-11-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11-1-111-1-11-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111-111-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-111111-1-11-1-11-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1111111-111-1-1-1-111-1-1-1-111
χ17222222222222222-2-2-2-22-222-2-2-2000000000002-200000000000000000
χ18222222222222222-2-2-2-22-2-2-2-22200000000000-2200000000000000000
χ19222222222222-2-2-222-2-2-2200-200000000002200000-2-20000000000000
χ20222222222222-2-2-222-2-2-2200-20000000000-2-200000220000000000000
χ21222222222222-2-2-2-2-222-2-20020000000000002000000-2-200200000000
χ22222222222222-2-2-2-2-222-2-2002000000000000-20000002200-200000000
χ2322222222-2-2-2-222-222-2-2-2-200200000000002-200000-220000000000000
χ2422222222-2-2-2-222-222-2-2-2-20020000000000-22000002-20000000000000
χ2522222222-2-2-2-222-2-2-222-2200-20000000000002000000-2200-200000000
χ2622222222-2-2-2-222-2-2-222-2200-2000000000000-20000002-200200000000
χ2722222222-2-2-2-2-2-22-2-2-2-222222-2-200000000000-2200000000000000000
χ2822222222-2-2-2-2-2-22-2-2-2-222-2-2222000000000002-200000000000000000
χ29222-22-2-2-2000000-22-22-2202i−2i02i−2i000022-2-2000000000002i−2i000000000
χ30222-22-2-2-2000000-22-22-2202i−2i02i−2i0000-2-22200000000000−2i2i000000000
χ31222-22-2-2-2000000-22-22-220−2i2i0−2i2i000022-2-200000000000−2i2i000000000
χ32222-22-2-2-2000000-22-22-220−2i2i0−2i2i0000-2-222000000000002i−2i000000000
χ33222-22-2-2-2000000-2-22-22202i−2i0−2i2i22-2-20000000002i−2i000000000000000
χ34222-22-2-2-2000000-2-22-22202i−2i0−2i2i-2-222000000000−2i2i000000000000000
χ35222-22-2-2-2000000-2-22-2220−2i2i02i−2i22-2-2000000000−2i2i000000000000000
χ36222-22-2-2-2000000-2-22-2220−2i2i02i−2i-2-2220000000002i−2i000000000000000
χ37444-44-4-4-400000044-4-44-4000000000000000000000000000000000000
χ38444-44-4-4-40000004-444-4-4000000000000000000000000000000000000
χ3944-4-4-44-4444-4-400000000000000000000000000000000000000002i−2i2i−2i
χ4044-4-4-44-4444-4-40000000000000000000000000000000000000000−2i2i−2i2i
χ4144-4-4-44-44-4-44400000000000000000000000000000000000000002i−2i−2i2i
χ4244-4-4-44-44-4-4440000000000000000000000000000000000000000−2i2i2i−2i
χ434-44-4-4-4444i−4i4i−4i0000000000000000000000000000000000002-22i−2i0000
χ444-44-4-4-4444i−4i4i−4i000000000000000000000000000000000000-22−2i2i0000
χ454-44-4-4-444−4i4i−4i4i0000000000000000000000000000000000002-2−2i2i0000
χ464-44-4-4-444−4i4i−4i4i000000000000000000000000000000000000-222i−2i0000
χ474-4-444-4-444i−4i−4i4i000000000000002i−2i2i−2i2-22-20000000000000000000000
χ484-4-444-4-444i−4i−4i4i00000000000000−2i2i−2i2i-22-220000000000000000000000
χ494-4-444-4-44−4i4i4i−4i000000000000002i−2i2i−2i-22-220000000000000000000000
χ504-4-444-4-44−4i4i4i−4i00000000000000−2i2i−2i2i2-22-20000000000000000000000
χ514-4-4-4444-400004i−4i0000000000002i−2i−2i2i2-2-220000000000000000000000
χ524-4-4-4444-400004i−4i000000000000−2i2i2i−2i-222-20000000000000000000000
χ534-4-4-4444-40000−4i4i0000000000002i−2i−2i2i-222-20000000000000000000000
χ544-4-4-4444-40000−4i4i000000000000−2i2i2i−2i2-2-220000000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-888-88-8-8000000000000000000000000000000000000000000000000

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