Finite Group Databasebeta

← Group #169839

Character table — Group #169839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444422444444888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-11111-1-1
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1111-1-1-1-111
χ911111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11-111-111-1-11-1
χ1011111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11-111-1-1-111-11
χ1111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-11-1-1111-1
χ1211111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-1111-1-1-11
χ1311111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-11-1-111-11
χ1411111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1111-1-11-1
χ1511111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1111-111-1-1-11
χ1611111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11-1111-1-1-1111-1
χ172222222222222-2-2-222-2-2-2-22-2000000000000000000000000020002-2-2000000
χ182222222222222-2-2-222-2-2-2-22-20000000000000000000000000-2000-222000000
χ19222222222222-2222-2-2-2-2-2-2-22000022220000000000000000000-2-2000000000
χ20222222222222-2222-2-2-2-2-2-2-220000-2-2-2-2000000000000000000022000000000
χ21222222222222-2-2-2-2-2-22222-2-2222200000000000000000000-20-200000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000020200000000000
χ2322222222-2-2-2-22-222-2-222-2-22-200000000000000000000000002000-22-2000000
χ2422222222-2-2-2-22-222-2-222-2-22-20000000000000000000000000-20002-22000000
χ2522222222-2-2-2-2-22-2-22222-2-2-22000022-2-20000000000000000000-22000000000
χ2622222222-2-2-2-2-22-2-22222-2-2-220000-2-22200000000000000000002-2000000000
χ2722222222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000000000-20200000000000
χ2822222222-2-2-2-2-2-22222-2-222-2-2-2-2220000000000000000000020-200000000000
χ2922-222-2-2-222-2-20-22-20000000200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000
χ3022-222-2-2-222-2-20-22-20000000200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000
χ3122-222-2-2-222-2-20-22-2000000020000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000
χ3222-222-2-2-222-2-20-22-2000000020000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000
χ3322-222-2-2-2-2-2220-2-220000000200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000
χ3422-222-2-2-2-2-2220-2-220000000200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000
χ3522-222-2-2-2-2-2220-2-22000000020000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000
χ3622-222-2-2-2-2-2220-2-22000000020000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000
χ372-2-22-222-22i−2i2i−2i0000002i−2i2-2002-22i−2i0000000000002−22−2i2−i2i2−i2000000002−2i2−i200
χ382-2-22-222-22i−2i2i−2i0000002i−2i2-2002-22i−2i000000000000−22−22−i2i2−i2i200000000−22−i2i200
χ392-2-22-222-22i−2i2i−2i0000002i−2i2-200-22−2i2i0000000000002−22−2i2−i2i2−i200000000−22−i2i200
χ402-2-22-222-22i−2i2i−2i0000002i−2i2-200-22−2i2i000000000000−22−22−i2i2−i2i2000000002−2i2−i200
χ412-2-22-222-2−2i2i−2i2i000000−2i2i2-2002-2−2i2i0000000000002−22−2−i2i2−i2i2000000002−2−i2i200
χ422-2-22-222-2−2i2i−2i2i000000−2i2i2-2002-2−2i2i000000000000−22−22i2−i2i2−i200000000−22i2−i200
χ432-2-22-222-2−2i2i−2i2i000000−2i2i2-200-222i−2i0000000000002−22−2−i2i2−i2i200000000−22i2−i200
χ442-2-22-222-2−2i2i−2i2i000000−2i2i2-200-222i−2i000000000000−22−22i2−i2i2−i2000000002−2−i2i200
χ45444-4-4-44-400004000000000-400000000022−2222−2200000000000000000000000000
χ46444-4-4-44-400004000000000-4000000000−2222−222200000000000000000000000000
χ47444-4-4-44-40000-4000000000400000000000002i2−2i22i2−2i20000000000000000000000
χ48444-4-4-44-40000-400000000040000000000000−2i22i2−2i22i20000000000000000000000
χ4944-444-4-4-444-4-404-440000000-400000000000000000000000000000000000000
χ5044-444-4-4-4-4-444044-40000000-400000000000000000000000000000000000000
χ5144-4-4-44-44000000004i−4i000000000000002i−2i−2i2i2-2-220000000000000000000000
χ5244-4-4-44-44000000004i−4i00000000000000−2i2i2i−2i-222-20000000000000000000000
χ5344-4-4-44-4400000000−4i4i000000000000002i−2i−2i2i-222-20000000000000000000000
χ5444-4-4-44-4400000000−4i4i00000000000000−2i2i2i−2i2-2-220000000000000000000000
χ554-444-4-4-444i−4i−4i4i00000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ564-444-4-4-444i−4i−4i4i0000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ574-444-4-4-44−4i4i4i−4i00000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ584-444-4-4-44−4i4i4i−4i0000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ594-4-44-444-44i−4i4i−4i000000−4i4i-440000000000000000000000000000000000000000
χ604-4-44-444-4−4i4i−4i4i0000004i−4i-440000000000000000000000000000000000000000
χ618-88-888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-88-888000000000000000000000000000000000000000000000000000000

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