Finite Group Databasebeta

← Group #336271

Character table — Group #336271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882222444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11-1-1-111-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-111111-1-1-1111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-11111-111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111111-11
χ11111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-1-111
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1111-1-111-11-1
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-11111-1-1-111-1-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-111-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-111-11-1-111111-1-1
χ172222222222-22-2-2-22-2-2222200220000-2-2000000000000-2000-22000000000
χ182222222222-22-2-2-22-2-2222200-2-20000-2-200000000000020002-2000000000
χ192222222222-22-2-2-22-2-2-2-2-2-200220000220000000000002000-2-2000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200-2-2000022000000000000-200022000000000
χ2122222222-2-22-2222-2-2-200002200-2-2220022-2-2000000000-20000000000000
χ2222222222-2-22-2222-2-2-200002200-2-2-2-200-2-22200000000020000000000000
χ2322222222-2-22-2222-2-2-20000-2-200222200-2-222000000000-20000000000000
χ2422222222-2-22-2222-2-2-20000-2-20022-2-20022-2-200000000020000000000000
χ2522-2-2-22-2200202-2-200022−2−200002i−2i2-22−2002i−2ii2i2−i2−i2i2i2−i2−i200000000002−2000
χ2622-2-2-22-2200202-2-200022−2−200002i−2i-222−200−2i2ii2i2−i2−i2−i2−i2i2i20000000000−22000
χ2722-2-2-22-2200202-2-200022−2−20000−2i2i2-22−200−2i2i−i2−i2i2i2−i2−i2i2i200000000002−2000
χ2822-2-2-22-2200202-2-200022−2−20000−2i2i-222−2002i−2i−i2−i2i2i2i2i2−i2−i20000000000−22000
χ2922-2-2-22-2200202-2-2000−2−22200002i−2i2-2−22002i−2i−i2−i2i2i2−i2−i2i2i20000000000−22000
χ3022-2-2-22-2200202-2-2000−2−22200002i−2i-22−2200−2i2i−i2−i2i2i2i2i2−i2−i200000000002−2000
χ3122-2-2-22-2200202-2-2000−2−2220000−2i2i2-2−2200−2i2ii2i2−i2−i2i2i2−i2−i20000000000−22000
χ3222-2-2-22-2200202-2-2000−2−2220000−2i2i-22−22002i−2ii2i2−i2−i2−i2−i2i2i200000000002−2000
χ332-222-2-2-2222-2-22-22-2-220000000000000000002i−2i2i−2i0000002i−2i00002-200000
χ342-222-2-2-2222-2-22-22-2-220000000000000000002i−2i2i−2i000000−2i2i0000-2200000
χ352-222-2-2-2222-2-22-22-2-22000000000000000000−2i2i−2i2i0000002i−2i0000-2200000
χ362-222-2-2-2222-2-22-22-2-22000000000000000000−2i2i−2i2i000000−2i2i00002-200000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ3844-444-4-4-44-404000-4000000004-4000000000000000000000000000000000
χ3944-444-4-4-44-404000-400000000-44000000000000000000000000000000000
χ4044-444-4-4-4-440-4000400000000000000000000000000000000002i2−2i20000000
χ4144-444-4-4-4-440-400040000000000000000000000000000000000−2i22i20000000
χ4244-4-4-44-4400-40-4440002222−22−2200000000−2222000000000000000000000000000
χ4344-4-4-44-4400-40-444000−22−2222220000000022−22000000000000000000000000000
χ444-444-4-4-44444-4-44-4-44-400000000000000000000000000000000000000000
χ454-444-4-4-44-4-444-44-44-4400000000000000000000000000000000000000000
χ464-444-4-4-44-4-4-444-4444-400000000000000000000000000000000000000000
χ474-44-444-4-400000000002i2−2i22i2−2i2000000000022−220000002i−2i2i−2i000000000000000
χ484-44-444-4-400000000002i2−2i22i2−2i20000000000−2222000000−2i2i−2i2i000000000000000
χ494-44-444-4-40000000000−2i22i2−2i22i2000000000022−22000000−2i2i−2i2i000000000000000
χ504-44-444-4-40000000000−2i22i2−2i22i20000000000−22220000002i−2i2i−2i000000000000000
χ514-4-44-444-44-40-4000400000000000000000000000022−22−2222000000000000000
χ524-4-44-444-44-40-40004000000000000000000000000−222222−22000000000000000
χ534-4-44-444-4-4404000-4004i−4i−4i4i0000000000000000000000000000000000000
χ544-4-44-444-4-4404000-400−4i4i4i−4i0000000000000000000000000000000000000
χ554-4-4-44-4440040-4-4400000004-400000000000000000000000000000000000
χ564-4-4-44-4440040-4-440000000-4400000000000000000000000000000000000
χ574-4-4-44-44400-4044-400000000000000000000022−22−22220000000000000000000
χ584-4-4-44-44400-4044-4000000000000000000000−222222−220000000000000000000
χ59888-8-8-88-8000000000000000000000000000000000000000000000000000

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