Finite Group Databasebeta

← Group #304271

Character table — Group #304271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444224444888888884444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-1-1-111111111111-11-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ9111111111111-1-1-1-111111111-1-11111-1-1-1-11-11-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111111-11-1-1-111-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-111
χ13111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-111111-1-111-1-1-1-111-1-111
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1-1-11111-1-111-1-1
χ1722222222222222-2-2-2-2-2-222-2-22-2000000000-202000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2222-200000000020-2000000000000000000
χ19222222222222-2-222-2-2-2-222-2-2-2200000000020-2000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-22000000000-202000000000000000000
χ2122222222-2-2-2-2222222-2-20000-2-2000000000000002-22-2000000000000
χ2222222222-2-2-2-2222222-2-20000-2-200000000000000-22-22000000000000
χ2322222222-2-2-2-222-2-2-2-2220000-220000000020-202-20000000000000000
χ2422222222-2-2-2-222-2-2-2-2220000-2200000000-2020-220000000000000000
χ2522222222-2-2-2-2-2-222-2-22200002-20000000020-20-220000000000000000
χ2622222222-2-2-2-2-2-222-2-22200002-200000000-20202-20000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2000022000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-200002200000000000000-222-2000000000000
χ29222-2-2-2-22-2-22200002-22-22-22-20000002i2i−2i−2i000000000000000000002i−2i
χ30222-2-2-2-22-2-22200002-22-22-22-2000000−2i−2i2i2i00000000000000000000−2i2i
χ31222-2-2-2-22-2-22200002-22-2-22-220000002i2i−2i−2i00000000000000000000−2i2i
χ32222-2-2-2-22-2-22200002-22-2-22-22000000−2i−2i2i2i000000000000000000002i−2i
χ33222-2-2-2-22-2-2220000-22-222-2-22002i2i−2i−2i00000000000000000000002i−2i00
χ34222-2-2-2-22-2-2220000-22-222-2-2200−2i−2i2i2i0000000000000000000000−2i2i00
χ35222-2-2-2-22-2-2220000-22-22-222-2002i2i−2i−2i0000000000000000000000−2i2i00
χ36222-2-2-2-22-2-2220000-22-22-222-200−2i−2i2i2i00000000000000000000002i−2i00
χ37444-4-4-4-4444-4-400004-4-44000000000000000000000000000000000000
χ38444-4-4-4-4444-4-40000-444-4000000000000000000000000000000000000
χ3944-444-4-4-44-44-400000000000000000022−2222−220000000000000000000000
χ4044-444-4-4-44-44-4000000000000000000−2222−22220000000000000000000000
χ4144-444-4-4-4-44-440000000000000022−2222−2200000000000000000000000000
χ4244-444-4-4-4-44-4400000000000000−2222−222200000000000000000000000000
χ4344-4-4-444-44-4-44000000000000002i2−2i2−2i22i200000000000000000000000000
χ4444-4-4-444-44-4-4400000000000000−2i22i22i2−2i200000000000000000000000000
χ4544-4-4-444-4-444-40000000000000000002i2−2i2−2i22i20000000000000000000000
χ4644-4-4-444-4-444-4000000000000000000−2i22i22i2−2i20000000000000000000000
χ474-44-444-4-400004-400000000000000000000000000000000002i−2i2i−2i0000
χ484-44-444-4-400004-40000000000000000000000000000000000−2i2i−2i2i0000
χ494-44-444-4-40000-4400000000000000000000000000000000002i−2i−2i2i0000
χ504-44-444-4-40000-440000000000000000000000000000000000−2i2i2i−2i0000
χ514-4-4-44-4440000004-400000000000000000000000000002-22-200000000
χ524-4-4-44-4440000004-40000000000000000000000000000-22-2200000000
χ534-4-4-44-444000000-4400000000000000000000000000002-2-2200000000
χ544-4-4-44-444000000-440000000000000000000000000000-222-200000000
χ558-888-8-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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