Finite Group Databasebeta

← Group #337306

Character table — Group #337306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-111-1
χ311111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1111111-1-1-1-1111111-11-1-11111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111-111
χ11111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-11-111-1-111-1-11-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-1-1-111-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-111-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1111-1-11111-11-1
χ172222222222-2-2-2-222-2-22222000022000000-2-200000000-220-200000000000
χ182222222222-2-2-2-222-2-222220000-2-2000000-2-2000000002-20200000000000
χ192222222222-2-2-2-222-2-2-2-2-2-20000220000002200000000-2-20200000000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000-2-20000002200000000220-200000000000
χ2122222222-2-22222-2-2-2-2000022-2-2002222-2-2000000000000-2000000000000
χ2222222222-2-22222-2-2-2-2000022-2-200-2-2-2-2220000000000002000000000000
χ2322222222-2-22222-2-2-2-20000-2-2220022-2-222000000000000-2000000000000
χ2422222222-2-22222-2-2-2-20000-2-22200-2-222-2-20000000000002000000000000
χ25222-2-22-2-2-2-222-2-2222-200000000000000000022-2-2000000002i−2i002i−2i00000
χ26222-2-22-2-2-2-222-2-2222-200000000000000000022-2-200000000−2i2i00−2i2i00000
χ27222-2-22-2-2-2-222-2-2222-2000000000000000000-2-222000000002i−2i00−2i2i00000
χ28222-2-22-2-2-2-222-2-2222-2000000000000000000-2-22200000000−2i2i002i−2i00000
χ2922-22-2-22-2002-22-20000i2i2−i2−i22-200002i−2i2i−2i00i2−i2i2−i2i2−i222−2−200000000002−2000
χ3022-22-2-22-2002-22-20000i2i2−i2−i22-20000−2i2i−2i2i00i2−i2i2−i2i2−i2−2−2220000000000−22000
χ3122-22-2-22-2002-22-20000i2i2−i2−i2-2200002i−2i−2i2i00i2−i2−i2i2−i2i2−2−22200000000002−2000
χ3222-22-2-22-2002-22-20000i2i2−i2−i2-220000−2i2i2i−2i00i2−i2−i2i2−i2i222−2−20000000000−22000
χ3322-22-2-22-2002-22-20000−i2−i2i2i22-200002i−2i2i−2i00−i2i2−i2i2−i2i2−2−2220000000000−22000
χ3422-22-2-22-2002-22-20000−i2−i2i2i22-20000−2i2i−2i2i00−i2i2−i2i2−i2i222−2−200000000002−2000
χ3522-22-2-22-2002-22-20000−i2−i2i2i2-2200002i−2i−2i2i00−i2i2i2−i2i2−i222−2−20000000000−22000
χ3622-22-2-22-2002-22-20000−i2−i2i2i2-220000−2i2i2i−2i00−i2i2i2−i2i2−i2−2−22200000000002−2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ39444-4-44-4-444-4-444-4-44-400000000000000000000000000000000000000000
χ40444-4-44-4-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ4144-44-4-44-400-44-4400002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ4244-44-4-44-400-44-440000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ4344-4-44-4-44004-4-4400000000000000000000002i2−2i2−2i22i20000000000000000000
χ4444-4-44-4-44004-4-440000000000000000000000−2i22i22i2−2i20000000000000000000
χ4544-4-44-4-4400-444-400000000004i−4i000000000000000000000000000000000
χ4644-4-44-4-4400-444-40000000000−4i4i000000000000000000000000000000000
χ474-444-4-4-444-400004-40000000000000000000000002i2−2i22i2−2i2000000000000000
χ484-444-4-4-444-400004-4000000000000000000000000−2i22i2−2i22i2000000000000000
χ494-444-4-4-44-440000-44004i−4i4i−4i0000000000000000000000000000000000000
χ504-444-4-4-44-440000-4400−4i4i−4i4i0000000000000000000000000000000000000
χ514-44-44-44-44-40000-4400000000000000000000000000000000002i2−2i20000000
χ524-44-44-44-44-40000-440000000000000000000000000000000000−2i22i20000000
χ534-44-44-44-4-4400004-400000000004i−4i0000000000000000000000000000000
χ544-44-44-44-4-4400004-40000000000−4i4i0000000000000000000000000000000
χ554-4-4444-4-4000000000022−22−222200000000002i2−2i20000002i−2i−2i2i000000000000000
χ564-4-4444-4-4000000000022−22−22220000000000−2i22i2000000−2i2i2i−2i000000000000000
χ574-4-4444-4-40000000000−222222−2200000000002i2−2i2000000−2i2i2i−2i000000000000000
χ584-4-4444-4-40000000000−222222−220000000000−2i22i20000002i−2i−2i2i000000000000000
χ598-8-8-8-8888000000000000000000000000000000000000000000000000000

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