Finite Group Databasebeta

← Group #170255

Character table — Group #170255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444422444444888888888888888824444444888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-11111-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-11-1-1-1-1-111
χ5111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-111-111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-111-1-1-11-1-1111-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-11-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1111-1-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1111-111-1-1-11
χ1722222222222222-2-2-2-2-2-2-2-22200000000000000000000000000202-20-2000000
χ1822222222222222-2-2-2-2-2-2-2-22200000000000000000000000000-20-2202000000
χ19222222222222-2-222-2-222-2-2-2-2220022000000000000000000000-200-20000000
χ20222222222222-2-222-2-222-2-2-2-2-2-200-2-200000000000000000000020020000000
χ21222222222222-2-2-2-222-2-222-2-2002200220000000000000000-2-2000000000000
χ22222222222222-2-2-2-222-2-222-2-200-2-200-2-2000000000000000022000000000000
χ2322222222-2-2-2-22222-2-2-2-222-2-2002200-2-200000000000000002-2000000000000
χ2422222222-2-2-2-22222-2-2-2-222-2-200-2-200220000000000000000-22000000000000
χ2522222222-2-2-2-222-2-22222-2-2-2-22200-2-2000000000000000000000-20020000000
χ2622222222-2-2-2-222-2-22222-2-2-2-2-2-20022000000000000000000000200-20000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000020-220-2000000
χ2822222222-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000-202-202000000
χ29222-2-2-22-22i2i−2i−2i002i−2i002-200002-2002i−2i00i2i2−i2−i222−2−20000000000000000i2−i22−200
χ30222-2-2-22-22i2i−2i−2i002i−2i002-200002-2002i−2i00−i2−i2i2i2−2−2220000000000000000−i2i2−2200
χ31222-2-2-22-22i2i−2i−2i002i−2i002-20000-2200−2i2i00i2i2−i2−i222−2−20000000000000000−i2i2−2200
χ32222-2-2-22-22i2i−2i−2i002i−2i002-20000-2200−2i2i00−i2−i2i2i2−2−2220000000000000000i2−i22−200
χ33222-2-2-22-2−2i−2i2i2i00−2i2i002-200002-200−2i2i00i2i2−i2−i2−2−2220000000000000000i2−i2−2200
χ34222-2-2-22-2−2i−2i2i2i00−2i2i002-200002-200−2i2i00−i2−i2i2i222−2−20000000000000000−i2i22−200
χ35222-2-2-22-2−2i−2i2i2i00−2i2i002-20000-22002i−2i00i2i2−i2−i2−2−2220000000000000000−i2i22−200
χ36222-2-2-22-2−2i−2i2i2i00−2i2i002-20000-22002i−2i00−i2−i2i2i222−2−20000000000000000i2−i2−2200
χ3722-2-222-2-22i−2i2i−2i00002i−2i002-200002-2002i−2i2−22−2i2−i2i2−i222−2−2i2i2−i2−i200000000000000
χ3822-2-222-2-22i−2i2i−2i00002i−2i002-200002-2002i−2i−22−22−i2i2−i2i2−2−222−i2−i2i2i200000000000000
χ3922-2-222-2-22i−2i2i−2i00002i−2i002-20000-2200−2i2i2−22−2i2−i2i2−i2−2−222−i2−i2i2i200000000000000
χ4022-2-222-2-22i−2i2i−2i00002i−2i002-20000-2200−2i2i−22−22−i2i2−i2i222−2−2i2i2−i2−i200000000000000
χ4122-2-222-2-2−2i2i−2i2i0000−2i2i002-200002-200−2i2i2−22−2−i2i2−i2i222−2−2−i2−i2i2i200000000000000
χ4222-2-222-2-2−2i2i−2i2i0000−2i2i002-200002-200−2i2i−22−22i2−i2i2−i2−2−222i2i2−i2−i200000000000000
χ4322-2-222-2-2−2i2i−2i2i0000−2i2i002-20000-22002i−2i2−22−2−i2i2−i2i2−2−222i2i2−i2−i200000000000000
χ4422-2-222-2-2−2i2i−2i2i0000−2i2i002-20000-22002i−2i−22−22i2−i2i2−i222−2−2−i2−i2i2i200000000000000
χ45444-4-4-44-44i4i−4i−4i00−4i4i00-44000000000000000000000000000000000000000000
χ46444-4-4-44-4−4i−4i4i4i004i−4i00-44000000000000000000000000000000000000000000
χ4744-44-4-4-444-4-44000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4844-44-4-4-444-4-4400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ4944-44-4-4-44-444-4000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ5044-44-4-4-44-444-400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ5144-4-444-4-44i−4i4i−4i0000−4i4i00-440000000000000000000000000000000000000000
χ5244-4-444-4-4−4i4i−4i4i00004i−4i00-440000000000000000000000000000000000000000
χ534-4444-4-4-400004i−4i000000000000000000000000002-22-22i−2i2i−2i00000000000000
χ544-4444-4-4-400004i−4i00000000000000000000000000-22-22−2i2i−2i2i00000000000000
χ554-4444-4-4-40000−4i4i000000000000000000000000002-22-2−2i2i−2i2i00000000000000
χ564-4444-4-4-40000−4i4i00000000000000000000000000-22-222i−2i2i−2i00000000000000
χ574-4-4-44-444000000000000004-40000000000000000000022−22−222200000000000000
χ584-4-4-44-444000000000000004-400000000000000000000−222222−2200000000000000
χ594-4-4-44-44400000000000000-44000000000000000022−22−2222000000000000000000
χ604-4-4-44-44400000000000000-440000000000000000−222222−22000000000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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