Finite Group Databasebeta

← Group #170350

Character table — Group #170350

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-11-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1111111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-11-1-11111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-11111-1-1-111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111-1
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
χ1722222222222222-2-2-2-2-2-222-2-22200220000000000000000000-20000-20000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-200-2-200000000000000000002000020000000
χ19222222222222-2-222-2-2-2-2-2-2220022002200000000000000000000-200-2000000
χ20222222222222-2-222-2-2-2-2-2-22200-2-200-2-2000000000000000000002002000000
χ21222222222222-2-2-2-22222-2-2-2-2000000000000000000000000202-20-200000000
χ22222222222222-2-2-2-22222-2-2-2-2000000000000000000000000-20-220200000000
χ2322222222-2-2-2-22222-2-222-2-2-2-200000000000000000000000020-220-200000000
χ2422222222-2-2-2-22222-2-222-2-2-2-2000000000000000000000000-202-20200000000
χ2522222222-2-2-2-222-2-222-2-2-2-222002200-2-200000000000000000000200-2000000
χ2622222222-2-2-2-222-2-222-2-2-2-22200-2-2002200000000000000000000-2002000000
χ2722222222-2-2-2-2-2-22222-2-222-2-22200-2-20000000000000000000-2000020000000
χ2822222222-2-2-2-2-2-22222-2-222-2-2-2-20022000000000000000000020000-20000000
χ2922-2-2-22-222i2i−2i−2i002i−2i0000002-2002i−2i002-2i2i2−i2−i222−2−200000000000000002−2i2−i200
χ3022-2-2-22-222i2i−2i−2i002i−2i0000002-2002i−2i002-2−i2−i2i2i2−2−2220000000000000000−22−i2i200
χ3122-2-2-22-222i2i−2i−2i002i−2i0000002-200−2i2i00-22i2i2−i2−i222−2−20000000000000000−22−i2i200
χ3222-2-2-22-222i2i−2i−2i002i−2i0000002-200−2i2i00-22−i2−i2i2i2−2−22200000000000000002−2i2−i200
χ3322-2-2-22-22−2i−2i2i2i00−2i2i0000002-2002i−2i00-22i2i2−i2−i2−2−22200000000000000002−2−i2i200
χ3422-2-2-22-22−2i−2i2i2i00−2i2i0000002-2002i−2i00-22−i2−i2i2i222−2−20000000000000000−22i2−i200
χ3522-2-2-22-22−2i−2i2i2i00−2i2i0000002-200−2i2i002-2i2i2−i2−i2−2−2220000000000000000−22i2−i200
χ3622-2-2-22-22−2i−2i2i2i00−2i2i0000002-200−2i2i002-2−i2−i2i2i222−2−200000000000000002−2−i2i200
χ372-22-2-222-22i−2i2i−2i2i−2i0000002-2002i−2i002-2002−22−2i2−i2i2−i2i2i2−i2−i222−2−200000000000000
χ382-22-2-222-22i−2i2i−2i2i−2i0000002-2002i−2i002-200−22−22−i2i2−i2i2−i2−i2i2i2−2−22200000000000000
χ392-22-2-222-22i−2i2i−2i2i−2i0000002-200−2i2i00-22002−22−2i2−i2i2−i2−i2−i2i2i2−2−22200000000000000
χ402-22-2-222-22i−2i2i−2i2i−2i0000002-200−2i2i00-2200−22−22−i2i2−i2i2i2i2−i2−i222−2−200000000000000
χ412-22-2-222-2−2i2i−2i2i−2i2i0000002-2002i−2i00-22002−22−2−i2i2−i2i2i2i2−i2−i2−2−22200000000000000
χ422-22-2-222-2−2i2i−2i2i−2i2i0000002-2002i−2i00-2200−22−22i2−i2i2−i2−i2−i2i2i222−2−200000000000000
χ432-22-2-222-2−2i2i−2i2i−2i2i0000002-200−2i2i002-2002−22−2−i2i2−i2i2−i2−i2i2i222−2−200000000000000
χ442-22-2-222-2−2i2i−2i2i−2i2i0000002-200−2i2i002-200−22−22i2−i2i2−i2i2i2−i2−i2−2−22200000000000000
χ454444-4-4-4-400000000004-40000000000000000000022−2222−22000000000000000000
χ464444-4-4-4-400000000004-400000000000000000000−2222−2222000000000000000000
χ474444-4-4-4-40000000000-4400000000000000000000000022−2222−2200000000000000
χ484444-4-4-4-40000000000-44000000000000000000000000−2222−222200000000000000
χ4944-4-4-44-444i4i−4i−4i00−4i4i000000-4400000000000000000000000000000000000000
χ5044-4-4-44-44−4i−4i4i4i004i−4i000000-4400000000000000000000000000000000000000
χ514-44-44-4-44000000004i−4i00000000000000000000002i−2i−2i2i2-2-2200000000000000
χ524-44-44-4-44000000004i−4i0000000000000000000000−2i2i2i−2i-222-200000000000000
χ534-44-44-4-4400000000−4i4i00000000000000000000002i−2i−2i2i-222-200000000000000
χ544-44-44-4-4400000000−4i4i0000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ554-44-4-444-44i−4i4i−4i−4i4i000000-440000000000000000000000000000000000000000
χ564-44-4-444-4−4i4i−4i4i4i−4i000000-440000000000000000000000000000000000000000
χ574-4-4444-4-44-4-44000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ584-4-4444-4-44-4-4400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ594-4-4444-4-4-444-4000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ604-4-4444-4-4-444-400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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