Finite Group Databasebeta

← Group #174306

Character table — Group #174306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888884444444444888844
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11111-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-11-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-111111-1-1
χ911111111-1-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11111-1-1-1-111-111-11-1-1-111-1-11-1
χ1011111111-1-1-1-111-1-11-1-1111-111-1-11111-1-1-1-11111-1-1-1-1-1-11-1-111-111-1-111-11
χ1111111111-1-1-1-111-1-11-1-1111-111-1-1-1-1-1-11111-1-1-1-1111111-111-11-1-1-1-1-111-11
χ1211111111-1-1-1-111-1-11-1-1111-111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-11111-1-11-1
χ1311111111-1-1-1-111-1-11-1-1111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-11-1111-1-1-11
χ1411111111-1-1-1-111-1-11-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-111-1-1-1111-1
χ1511111111-1-1-1-111-1-11-1-1111-1-1-111-1-1-1-111111111-1-1-1-111-1-1-11-11-11-1-1111-1
χ1611111111-1-1-1-111-1-11-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-111-111-1-1-11
χ172222222222222-2-2-2-2-2-22-2-2222-2-20000000000000000000000-2200000000
χ182222222222222-2-2-2-2-2-22-2-22-2-22200000000000000000000002-200000000
χ19222222222222-2222-2-2-2-22-2-2000000000000000000000002-22000-2000000
χ20222222222222-2222-2-2-2-22-2-200000000000000000000000-22-20002000000
χ21222222222222-2-2-2-2222-2-22-2000000000000000000002-2200000-20000000
χ22222222222222-2-2-2-2222-2-22-200000000000000000000-22-20000020000000
χ2322222222-2-2-2-22-222-2222-2-2-222220000000000000000000000-2-200000000
χ2422222222-2-2-2-22-222-2222-2-2-2-2-2-2-200000000000000000000002200000000
χ2522222222-2-2-2-2-22-2-2-222-22-22000000000000000000000002-2-20002000000
χ2622222222-2-2-2-2-22-2-2-222-22-2200000000000000000000000-222000-2000000
χ2722222222-2-2-2-2-2-2222-2-2-2-222000000000000000000002-2-20000020000000
χ2822222222-2-2-2-2-2-2222-2-2-2-22200000000000000000000-22200000-20000000
χ29222-2-2-22-20000-202-202-220002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ30222-2-2-22-20000-202-202-220002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ31222-2-2-22-20000-202-202-22000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ32222-2-2-22-20000-202-202-22000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ33222-2-2-22-20000-20-220-2220002-2-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ34222-2-2-22-20000-20-220-2220002-2-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ35222-2-2-22-20000-20-220-222000-222-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ36222-2-2-22-20000-20-220-222000-222-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ37444-4-4-44-40000404-40-44-4000000000000000000000000000000000000000
χ38444-4-4-44-4000040-4404-4-4000000000000000000000000000000000000000
χ3944-444-4-4-444-4-4000000000000000000000000000000000000000002-22-200
χ4044-444-4-4-444-4-400000000000000000000000000000000000000000-22-2200
χ4144-444-4-4-4-4-444000000000000000000000000000000000000000002-2-2200
χ4244-444-4-4-4-4-44400000000000000000000000000000000000000000-222-200
χ434-444-44-4-4000004000000-40000000000000022−2222−2200000000000000000000
χ444-444-44-4-4000004000000-400000000000000−2222−222200000000000000000000
χ454-444-44-4-400000-400000040000000000000000002i2−2i22i2−2i20000000000000000
χ464-444-44-4-400000-40000004000000000000000000−2i22i2−2i22i20000000000000000
χ474-44-44-4-444i−4i4i−4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ484-44-44-4-444i−4i4i−4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ494-44-44-4-44−4i4i−4i4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ504-44-44-4-44−4i4i−4i4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ514-4-44-4-4440000000040000-40000000002i2−2i22i2−2i2000000000000000000000000
χ524-4-44-4-4440000000040000-4000000000−2i22i2−2i22i2000000000000000000000000
χ534-4-44-4-44400000000-4000040000022−2222−220000000000000000000000000000
χ544-4-44-4-44400000000-40000400000−2222−22220000000000000000000000000000
χ554-4-4-4444-44i−4i−4i4i0000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ564-4-4-4444-44i−4i−4i4i000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ574-4-4-4444-4−4i4i4i−4i0000000000000002i−2i−2i2i-222-2000000000000000000000000
χ584-4-4-4444-4−4i4i4i−4i000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ5988-8-8-88-88000000000000000000000000000000000000000000000000000

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