Finite Group Databasebeta

← Group #166558

Character table — Group #166558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444442244444448888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111
χ51111111111111111111111-1-1111-1-111111111111-1-111-1-11-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-111111-111-1-1-1-11111-1-1-1-111-1111-1-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-111111-111-1-1-1-1-1-1-1-1111111-1-1-11-1-11-111-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-11-1-11-11-111111-1-1-1-111
χ1211111111-1-1-1-1111-1-1-1-111111-1-1-1-1-111-1-1-1-11111-1-11111-11-11-1-1-1-11111-1-1
χ1311111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-11111-1-1-1-11-1111-11-1-11-1-1-1-111-1-111
χ1411111111-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-1-1-111111-11-1-1-11-1-111111-1-111-1-1
χ1511111111-1-1-1-1111-1-1-1-1111-1-1-1-1-111111111-1-1-1-1-11-1-1-1-1111-111-1-11111-1-1
χ1611111111-1-1-1-1111-1-1-1-1111-1-1-1-1-11111-1-1-1-11111-11-111-1111-1-1-111-1-1-1-111
χ172222222222222-2-222-2-22-2-200-22200-2-200000000-20000002000000000000
χ182222222222222-2-222-2-22-2-200-2-2-20022000000002000000-2000000000000
χ19222222222222-22-2-2-222-22-222-20022000000000000000-2-20000000000000
χ20222222222222-22-2-2-222-22-2-2-2-200-2-2000000000000000220000000000000
χ21222222222222-2-22-2-2-2-2-2-220020000000000000002200000-2-20000000000
χ22222222222222-2-22-2-2-2-2-2-22002000000000000000-2-200000220000000000
χ2322222222-2-2-2-22-2-2-2-2222-2-200222002200000000-2000000-2000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-2002-2-200-2-20000000020000002000000000000
χ2522222222-2-2-2-2-22-222-2-2-22-222200-2-2000000000000000-220000000000000
χ2622222222-2-2-2-2-22-222-2-2-22-2-2-2200220000000000000002-20000000000000
χ2722222222-2-2-2-2-2-222222-2-2200-20000000000000002-200000-220000000000
χ2822222222-2-2-2-2-2-222222-2-2200-2000000000000000-22000002-20000000000
χ29222-2-22-2-222-2-20-20002-20202-20002-200i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i20000
χ30222-2-22-2-222-2-20-20002-20202-20002-200−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i20000
χ31222-2-22-2-222-2-20-20002-2020-22000-2200i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i20000
χ32222-2-22-2-222-2-20-20002-2020-22000-2200−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i20000
χ33222-2-22-2-2-2-2220-2000-220202-2000-2200i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i20000
χ34222-2-22-2-2-2-2220-2000-220202-2000-2200−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i20000
χ35222-2-22-2-2-2-2220-2000-22020-220002-200i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i20000
χ36222-2-22-2-2-2-2220-2000-22020-220002-200−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i20000
χ37444-4-44-4-444-4-404000-440-400000000000000000000000000000000000000
χ38444-4-44-4-4-4-444040004-40-400000000000000000000000000000000000000
χ3944-44-4-44-400004000000-40000000004-40000000000000000000000000000
χ4044-44-4-44-400004000000-4000000000-440000000000000000000000000000
χ4144-44-4-44-40000-40000004000004i−4i00000000000000000000000000000000
χ4244-44-4-44-40000-4000000400000−4i4i00000000000000000000000000000000
χ434-444-4-4-444i−4i4i−4i0000000000000000000000000000002-2000002i−2i00000000
χ444-444-4-4-444i−4i4i−4i000000000000000000000000000000-2200000−2i2i00000000
χ454-444-4-4-44−4i4i−4i4i0000000000000000000000000000002-200000−2i2i00000000
χ464-444-4-4-44−4i4i−4i4i000000000000000000000000000000-22000002i−2i00000000
χ474-44-44-44-44i−4i−4i4i00000000000000000000000000000000000000000002-22i−2i
χ484-44-44-44-44i−4i−4i4i0000000000000000000000000000000000000000000-22−2i2i
χ494-44-44-44-4−4i4i4i−4i00000000000000000000000000000000000000000002-2−2i2i
χ504-44-44-44-4−4i4i4i−4i0000000000000000000000000000000000000000000-222i−2i
χ514-4-4444-4-400000004i−4i000000000000002i−2i2i−2i2-22-200000000000000000000
χ524-4-4444-4-400000004i−4i00000000000000−2i2i−2i2i-22-2200000000000000000000
χ534-4-4444-4-40000000−4i4i000000000000002i−2i2i−2i-22-2200000000000000000000
χ544-4-4444-4-40000000−4i4i00000000000000−2i2i−2i2i2-22-200000000000000000000
χ554-4-4-4-44440000004000000-400000000000002i2−2i2−2i22i200000000000000000000
χ564-4-4-4-44440000004000000-40000000000000−2i22i22i2−2i200000000000000000000
χ574-4-4-4-4444000000-4000000400000000022−22−2222000000000000000000000000
χ584-4-4-4-4444000000-40000004000000000−222222−22000000000000000000000000
χ5988-8-88-8-88000000000000000000000000000000000000000000000000000

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