Finite Group Databasebeta

← Group #336994

Character table — Group #336994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-1-111-1
χ311111111111111111111111111-1-11111111111111111-11-1-1-1-111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1111111111-1-1-111-1-11111-1-1-1
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
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1111-11-1-111-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-111
χ11111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-1111-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111-11111-1-11-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1111-11-1-1-1-1111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11-1-1-111-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-111-1-111-11-1
χ172222222222-2-2-2-222-2-2000022-2-2002200000022-2-200000-20000000000000
χ182222222222-2-2-2-222-2-2000022-2-200-2-2000000-2-2220000020000000000000
χ192222222222-2-2-2-222-2-20000-2-2220022000000-2-22200000-20000000000000
χ202222222222-2-2-2-222-2-20000-2-22200-2-200000022-2-20000020000000000000
χ2122222222-2-22222-2-2-2-2222200002200-2-20000000000002000-2-2000000000
χ2222222222-2-22222-2-2-2-222220000-2-200-2-2000000000000-200022000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000220022000000000000-20002-2000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000-2-200220000000000002000-22000000000
χ252-222-2-22-2-2-222-2-2222-2000000000000002i2i−2i−2i00000000002i−2i0000002-2000
χ262-222-2-22-2-2-222-2-2222-2000000000000002i2i−2i−2i0000000000−2i2i000000-22000
χ272-222-2-22-2-2-222-2-2222-200000000000000−2i−2i2i2i00000000002i−2i000000-22000
χ282-222-2-22-2-2-222-2-2222-200000000000000−2i−2i2i2i0000000000−2i2i0000002-2000
χ292-22-22-2-222-200002-200i2i2−i2−i2002-2002i−2ii2−i2i2−i2i2−i2002i−2i22−2−20000002−20000000
χ302-22-22-2-222-200002-200i2i2−i2−i2002-200−2i2ii2−i2i2−i2i2−i200−2i2i−2−222000000−220000000
χ312-22-22-2-222-200002-200i2i2−i2−i200-22002i−2ii2−i2−i2i2−i2i200−2i2i−2−2220000002−20000000
χ322-22-22-2-222-200002-200i2i2−i2−i200-2200−2i2ii2−i2−i2i2−i2i2002i−2i22−2−2000000−220000000
χ332-22-22-2-222-200002-200−i2−i2i2i2002-2002i−2i−i2i2−i2i2−i2i2002i−2i−2−222000000−220000000
χ342-22-22-2-222-200002-200−i2−i2i2i2002-200−2i2i−i2i2−i2i2−i2i200−2i2i22−2−20000002−20000000
χ352-22-22-2-222-200002-200−i2−i2i2i200-22002i−2i−i2i2i2−i2i2−i200−2i2i22−2−2000000−220000000
χ362-22-22-2-222-200002-200−i2−i2i2i200-2200−2i2i−i2i2i2−i2i2−i2002i−2i−2−2220000002−20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-44-40000-440000004-400000000000000000000000000000000000
χ39444-4-44-4-44-40000-44000000-4400000000000000000000000000000000000
χ40444-4-44-4-4-4400004-4000000000000000022−22−222200000000000000000000000
χ41444-4-44-4-4-4400004-40000000000000000−222222−2200000000000000000000000
χ4244-444-4-4-4004-44-40000000000000000000000000022−2222−22000000000000000
χ4344-444-4-4-4004-44-400000000000000000000000000−2222−2222000000000000000
χ4444-444-4-4-400-44-4400004-44-40000000000000000000000000000000000000
χ4544-444-4-4-400-44-440000-44-440000000000000000000000000000000000000
χ464-444-4-44-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ474-444-4-44-444-4-444-4-44-400000000000000000000000000000000000000000
χ484-444-4-44-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ494-44-44-4-44-440000-44002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ504-44-44-4-44-440000-4400−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ514-4-44-44-44004-4-440000000000004i−4i0000000000000000000000000000000
χ524-4-44-44-44004-4-44000000000000−4i4i0000000000000000000000000000000
χ534-4-44-44-4400-444-4000000000000000000000000000000000000002i2−2i200000
χ544-4-44-44-4400-444-400000000000000000000000000000000000000−2i22i200000
χ554-4-4-4444-400000000002i2−2i2−2i22i2000000000000002i2−2i2002-2-22000000000000000
χ564-4-4-4444-400000000002i2−2i2−2i22i200000000000000−2i22i200-222-2000000000000000
χ574-4-4-4444-40000000000−2i22i22i2−2i2000000000000002i2−2i200-222-2000000000000000
χ584-4-4-4444-40000000000−2i22i22i2−2i200000000000000−2i22i2002-2-22000000000000000
χ5988-8-8-8-888000000000000000000000000000000000000000000000000000

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