Finite Group Databasebeta

← Group #170309

Character table — Group #170309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444422444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-11-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-11-111111-1-1
χ911111111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-111-111-1-11-1
χ1011111111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-111-1-1-111-11
χ1111111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-11
χ1211111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-1111-1
χ1311111111-1-1-1-11-1-1-1-11-1-11111-1-11111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-111-1-111-11
χ1411111111-1-1-1-11-1-1-1-11-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-11-1
χ1511111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ1611111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-11
χ17222222222222222-2-2-2-2-2-2-22-2000000000000000000000000200-2020-2000000
χ18222222222222222-2-2-2-2-2-2-22-2000000000000000000000000-20020-202000000
χ19222222222222-2-2-222-2-2-222-2-20000222200000000000000000000-20-20000000
χ20222222222222-2-2-222-2-2-222-2-20000-2-2-2-2000000000000000000002020000000
χ21222222222222-2-2-2-2-2222-2-2-222222000000000000000000000-2-200000000000
χ22222222222222-2-2-2-2-2222-2-2-22-2-2-2-20000000000000000000002200000000000
χ2322222222-2-2-2-22-2-222-222-2-22-200000000000000000000000020020-20-2000000
χ2422222222-2-2-2-22-2-222-222-2-22-2000000000000000000000000-200-20202000000
χ2522222222-2-2-2-2-222222-2-2-2-2-2222-2-2000000000000000000000-2200000000000
χ2622222222-2-2-2-2-222222-2-2-2-2-22-2-2220000000000000000000002-200000000000
χ2722222222-2-2-2-2-222-2-2-22222-2-2000022-2-20000000000000000000020-20000000
χ2822222222-2-2-2-2-222-2-2-22222-2-20000-2-22200000000000000000000-2020000000
χ2922-22-2-2-222i2i−2i−2i0002i−2i0002-20000002i−2i2-222−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000000000
χ3022-22-2-2-222i2i−2i−2i0002i−2i0002-20000002i−2i2-2−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000000000
χ3122-22-2-2-222i2i−2i−2i0002i−2i0002-2000000−2i2i-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000
χ3222-22-2-2-222i2i−2i−2i0002i−2i0002-2000000−2i2i-22−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000
χ3322-22-2-2-22−2i−2i2i2i000−2i2i0002-20000002i−2i-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000
χ3422-22-2-2-22−2i−2i2i2i000−2i2i0002-20000002i−2i-22−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000
χ3522-22-2-2-22−2i−2i2i2i000−2i2i0002-2000000−2i2i2-222−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000000000
χ3622-22-2-2-22−2i−2i2i2i000−2i2i0002-2000000−2i2i2-2−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000000000
χ372-2-2-2-22222-22-200000-22-200022-22-200002−22−22−22−200000000000000002−22−200
χ382-2-2-2-22222-22-200000-22-200022-22-20000−22−22−22−220000000000000000−22−2200
χ392-2-2-2-22222-22-200000-22-20002-22-2200002−22−22−22−20000000000000000−22−2200
χ402-2-2-2-22222-22-200000-22-20002-22-220000−22−22−22−2200000000000000002−22−200
χ412-2-2-2-2222-22-2200000-2-2200022-2-2200002−22−2−22−2200000000000000002−2−2200
χ422-2-2-2-2222-22-2200000-2-2200022-2-220000−22−222−22−20000000000000000−222−200
χ432-2-2-2-2222-22-2200000-2-220002-222-200002−22−2−22−220000000000000000−222−200
χ442-2-2-2-2222-22-2200000-2-220002-222-20000−22−222−22−200000000000000002−2−2200
χ4544-44-4-4-444i4i−4i−4i000−4i4i000-440000000000000000000000000000000000000000
χ4644-44-4-4-44−4i−4i4i4i0004i−4i000-440000000000000000000000000000000000000000
χ474-444-44-4-400004000000000-40000000000000000022−2222−22000000000000000000
χ484-444-44-4-400004000000000-400000000000000000−2222−2222000000000000000000
χ494-444-44-4-40000-400000000040000000000000000000002i2−2i22i2−2i200000000000000
χ504-444-44-4-40000-40000000004000000000000000000000−2i22i2−2i22i200000000000000
χ514-44-44-4-444i−4i−4i4i000000000000000000002-2-222i−2i−2i2i0000000000000000000000
χ524-44-44-4-444i−4i−4i4i00000000000000000000-222-2−2i2i2i−2i0000000000000000000000
χ534-44-44-4-44−4i4i4i−4i000000000000000000002-2-22−2i2i2i−2i0000000000000000000000
χ544-44-44-4-44−4i4i4i−4i00000000000000000000-222-22i−2i−2i2i0000000000000000000000
χ554-4-444-44-4000004-400000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ564-4-444-44-4000004-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ574-4-444-44-400000-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ584-4-444-44-400000-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-4-4-4-44444-44-4000004-44000-400000000000000000000000000000000000000
χ604-4-4-4-4444-44-440000044-4000-400000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-888-8-8000000000000000000000000000000000000000000000000000000

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