Finite Group Databasebeta

← Group #337182

Character table — Group #337182

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-111
χ51111111111111111111111-1-1111111-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1
χ71111111111111111111111-1-1-1-111-1-1111111-1-1-1-11111-1111-1-11111-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-111-1-1-1-11-11
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-111111-11
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-11-1-1-1-111-1-11111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-11
χ172222222222-2-2-2-222-2-22222000022000000-2-2000000000-2-2200000000000
χ182222222222-2-2-2-222-2-222220000-2-2000000-2-200000000022-200000000000
χ192222222222-2-2-2-222-2-2-2-2-2-200002200000022000000000-22-200000000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000-2-2000000220000000002-2200000000000
χ2122222222-2-22222-2-2-2-20000222200-2-222-2-20000000000-200000000000000
χ2222222222-2-22222-2-2-2-2000022-2-20022-2-2220000000000-200000000000000
χ2322222222-2-22222-2-2-2-20000-2-22200-2-2-2-2220000000000200000000000000
χ2422222222-2-22222-2-2-2-20000-2-2-2-2002222-2-20000000000200000000000000
χ252-22-22-22-2-2-222-2-2222-200000000000000000022-2-2000000002i−2i002i−2i00000
χ262-22-22-22-2-2-222-2-2222-200000000000000000022-2-200000000−2i2i00−2i2i00000
χ272-22-22-22-2-2-222-2-2222-2000000000000000000-2-222000000002i−2i00−2i2i00000
χ282-22-22-22-2-2-222-2-2222-2000000000000000000-2-22200000000−2i2i002i−2i00000
χ292-2-22-222-2002-22-20000i2i2−i2−i22-200002-2002-2i2−i2i2−i2i2−i2i2i2−i2−i20000000000i2−i2000
χ302-2-22-222-2002-22-20000i2i2−i2−i22-20000-2200-22i2−i2−i2i2−i2i2−i2−i2i2i20000000000i2−i2000
χ312-2-22-222-2002-22-20000i2i2−i2−i2-2200002-200-22i2−i2i2−i2i2−i2−i2−i2i2i20000000000−i2i2000
χ322-2-22-222-2002-22-20000i2i2−i2−i2-220000-22002-2i2−i2−i2i2−i2i2i2i2−i2−i20000000000−i2i2000
χ332-2-22-222-2002-22-20000−i2−i2i2i22-200002-2002-2−i2i2−i2i2−i2i2−i2−i2i2i20000000000−i2i2000
χ342-2-22-222-2002-22-20000−i2−i2i2i22-20000-2200-22−i2i2i2−i2i2−i2i2i2−i2−i20000000000−i2i2000
χ352-2-22-222-2002-22-20000−i2−i2i2i2-2200002-200-22−i2i2−i2i2−i2i2i2i2−i2−i20000000000i2−i2000
χ362-2-22-222-2002-22-20000−i2−i2i2i2-220000-22002-2−i2i2i2−i2i2−i2−i2−i2i2i20000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-44-400004-400000000000000000000000022−2222−22000000000000000
χ394444-4-4-4-44-400004-4000000000000000000000000−2222−2222000000000000000
χ404444-4-4-4-4-440000-44004-44-40000000000000000000000000000000000000
χ414444-4-4-4-4-440000-4400-44-440000000000000000000000000000000000000
χ4244-4-4-4-444004-4-4400000000000000000000002i2−2i2−2i22i20000000000000000000
χ4344-4-4-4-444004-4-440000000000000000000000−2i22i22i2−2i20000000000000000000
χ4444-4-4-4-44400-444-400000000004i−4i000000000000000000000000000000000
χ4544-4-4-4-44400-444-40000000000−4i4i000000000000000000000000000000000
χ464-44-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ474-44-44-44-444-4-444-4-44-400000000000000000000000000000000000000000
χ484-44-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ494-44-4-44-444-40000-4400000000000000000000000000000000002i2−2i20000000
χ504-44-4-44-444-40000-440000000000000000000000000000000000−2i22i20000000
χ514-44-4-44-44-4400004-400000000004i−4i0000000000000000000000000000000
χ524-44-4-44-44-4400004-40000000000−4i4i0000000000000000000000000000000
χ534-4-444-4-4400000000002i2−2i2−2i22i20000000022−22000000002i−2i−2i2i000000000000000
χ544-4-444-4-4400000000002i2−2i2−2i22i200000000−222200000000−2i2i2i−2i000000000000000
χ554-4-444-4-440000000000−2i22i22i2−2i20000000022−2200000000−2i2i2i−2i000000000000000
χ564-4-444-4-440000000000−2i22i22i2−2i200000000−2222000000002i−2i−2i2i000000000000000
χ574-4-44-444-400-44-4400002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ584-4-44-444-400-44-440000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ5988-8-888-8-8000000000000000000000000000000000000000000000000000

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