Finite Group Databasebeta

← Group #173697

Character table — Group #173697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444444444444444444444488888888888824
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ911111111-1-1-1-11-1-111111-111-1-111-1-111-1-11-11-11-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-111111-111-1-111-1-111-1-11-11-11-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-11-1-111111-111-1-1-1-111-1-111-111-1-1111-1-1-1-11111-1-1-11
χ1211111111-1-1-1-11-1-111111-111-1-1-1-111-1-111-111-1-11-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-11-1-111111-1-1-11111-1-1-1-111-11-111-111-1-1-1-111-1-1111-1
χ1411111111-1-1-1-11-1-111111-1-1-11111-1-1-1-111-11-111-1-1-11111-1-111-1-1-11
χ1511111111-1-1-1-11-1-111111-1-1-111-1-11111-1-11-1-11-1111-1-111-1-1-1-111-11
χ1611111111-1-1-1-11-1-111111-1-1-111-1-11111-1-11-1-11-11-1-111-1-11111-1-11-1
χ172222222222222-2-2-2-2-2-22-2000000002222-2-2000000000000000000
χ182222222222222-2-2-2-2-2-22-200000000-2-2-2-222000000000000000000
χ192222222222-2-2-22222-2-2-2-20000222200000000-2-200000000000000
χ202222222222-2-2-22222-2-2-2-20000-2-2-2-2000000002200000000000000
χ212222222222-2-2-2-2-2-2-222-2222-2-20000000000-220000000000000000
χ222222222222-2-2-2-2-2-2-222-22-2-22200000000002-20000000000000000
χ2322222222-2-222-222-2-222-2-222220000000000-2-20000000000000000
χ2422222222-2-222-222-2-222-2-2-2-2-2-20000000000220000000000000000
χ2522222222-2-222-2-2-222-2-2-22000022-2-200000000-2200000000000000
χ2622222222-2-222-2-2-222-2-2-220000-2-222000000002-200000000000000
χ2722222222-2-2-2-2222-2-2-2-2220000000022-2-2-22000000000000000000
χ2822222222-2-2-2-2222-2-2-2-22200000000-2-2222-2000000000000000000
χ29222-2-2-22-22-22-2-200000020000000002-22-2000000i2−i2i2−i2i2−i2i2−i2000000
χ30222-2-2-22-22-22-2-200000020000000002-22-2000000−i2i2−i2i2−i2i2−i2i2000000
χ31222-2-2-22-22-22-2-20000002000000000-22-22000000i2−i2i2−i2−i2i2−i2i2000000
χ32222-2-2-22-22-22-2-20000002000000000-22-22000000−i2i2−i2i2i2−i2i2−i2000000
χ33222-2-2-22-2-22-22-200000020000000002-2-22000000i2−i2−i2i2i2−i2−i2i2000000
χ34222-2-2-22-2-22-22-200000020000000002-2-22000000−i2i2i2−i2−i2i2i2−i2000000
χ35222-2-2-22-2-22-22-20000002000000000-222-2000000i2−i2−i2i2−i2i2i2−i2000000
χ36222-2-2-22-2-22-22-20000002000000000-222-2000000−i2i2i2−i2i2−i2−i2i2000000
χ37444-4-4-44-44-4-444000000-4000000000000000000000000000000000
χ38444-4-4-44-4-444-44000000-4000000000000000000000000000000000
χ3944-44-4-4-4400000004-400000000004i−4i000000000000000000000000
χ4044-44-4-4-4400000004-40000000000−4i4i000000000000000000000000
χ4144-44-4-4-440000000-44000000004i−4i00000000000000000000000000
χ4244-44-4-4-440000000-4400000000−4i4i00000000000000000000000000
χ434-44-44-4-440000000004-400004i−4i0000000000000000000000000000
χ444-44-44-4-440000000004-40000−4i4i0000000000000000000000000000
χ454-44-44-4-44000000000-44004i−4i000000000000000000000000000000
χ464-44-44-4-44000000000-4400−4i4i000000000000000000000000000000
χ474-4-4-4-4444000004-4000000000000000000000000000000002-22-200
χ484-4-4-4-4444000004-400000000000000000000000000000000-22-2200
χ494-4-4-4-444400000-44000000000000000000000000000000002-2-2200
χ504-4-4-4-444400000-4400000000000000000000000000000000-222-200
χ5188-8-888-8-8000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-888-88-8000000000000000000000000000000000000000000000

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