Finite Group Databasebeta

← Group #337190

Character table — Group #337190

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111111111111-1-1-1-11-1-1-1-1-111-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111111-111
χ51111111111111111111111-1-1111111-1-1-1-1111111-1-1-1-111-1-1-11-1-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-11-1-1
χ71111111111111111111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-111111-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1111-111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-11-11
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1111-1-1-111-1-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-1-111-1
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1111111-1
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1111-1-111-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-1-1-111-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1111-11-1-11111-11-1
χ1722222222222-2-2-2-22-2-22222000022000000-2-200000000-22000-2000000000
χ1822222222222-2-2-2-22-2-222220000-2-2000000-2-2000000002-20002000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000220000002200000000-2-20002000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-20000-2-2000000220000000022000-2000000000
χ2122222222-2-2-22222-2-2-20000222200-2-222-2-200000000000000-20000000000
χ2222222222-2-2-22222-2-2-2000022-2-20022-2-22200000000000000-20000000000
χ2322222222-2-2-22222-2-2-20000-2-22200-2-2-2-2220000000000000020000000000
χ2422222222-2-2-22222-2-2-20000-2-2-2-2002222-2-20000000000000020000000000
χ2522-2-22-2-22-2-2222-2-222-200000000000000000022-2-20000002i−2i00002i−2i00000
χ2622-2-22-2-22-2-2222-2-222-200000000000000000022-2-2000000−2i2i0000−2i2i00000
χ2722-2-22-2-22-2-2222-2-222-2000000000000000000-2-2220000002i−2i0000−2i2i00000
χ2822-2-22-2-22-2-2222-2-222-2000000000000000000-2-222000000−2i2i00002i−2i00000
χ292-22-2-22-220002-22-2000i2i2−i2−i22-200002-2002-2i2−i2i2−i2i2−i2i2i2−i2−i20000000000i2−i2000
χ302-22-2-22-220002-22-2000i2i2−i2−i22-20000-2200-22i2−i2−i2i2−i2i2−i2−i2i2i20000000000i2−i2000
χ312-22-2-22-220002-22-2000i2i2−i2−i2-2200002-200-22i2−i2i2−i2i2−i2−i2−i2i2i20000000000−i2i2000
χ322-22-2-22-220002-22-2000i2i2−i2−i2-220000-22002-2i2−i2−i2i2−i2i2i2i2−i2−i20000000000−i2i2000
χ332-22-2-22-220002-22-2000−i2−i2i2i22-200002-2002-2−i2i2−i2i2−i2i2−i2−i2i2i20000000000−i2i2000
χ342-22-2-22-220002-22-2000−i2−i2i2i22-20000-2200-22−i2i2i2−i2i2−i2i2i2−i2−i20000000000−i2i2000
χ352-22-2-22-220002-22-2000−i2−i2i2i2-2200002-200-22−i2i2−i2i2−i2i2i2i2−i2−i20000000000i2−i2000
χ362-22-2-22-220002-22-2000−i2−i2i2i2-220000-22002-2−i2i2i2−i2i2−i2−i2−i2i2i20000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-44-44-440000-4000000000000000000000000000000000022−220000000
χ39444-4-4-44-44-440000-40000000000000000000000000000000000−22220000000
χ40444-4-4-44-4-44-40000400000000004i−4i0000000000000000000000000000000
χ41444-4-4-44-4-44-4000040000000000−4i4i0000000000000000000000000000000
χ4244-44-44-4-44-4-4000040000000000000000000000002i2−2i22i2−2i2000000000000000
χ4344-44-44-4-44-4-400004000000000000000000000000−2i22i2−2i22i2000000000000000
χ4444-44-44-4-4-4440000-4004-44-40000000000000000000000000000000000000
χ4544-44-44-4-4-4440000-400-44-440000000000000000000000000000000000000
χ4644-4-44-4-4444-444-4-4-4-4400000000000000000000000000000000000000000
χ4744-4-44-4-4444-4-4-444-44-400000000000000000000000000000000000000000
χ4844-4-44-4-44-4-44-4-4444-4400000000000000000000000000000000000000000
χ494-44-4-44-44000-44-440002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ504-44-4-44-44000-44-44000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ514-4-44-4-4440004-4-440000000000000000000002i2−2i2−2i22i20000000000000000000
χ524-4-44-4-4440004-4-44000000000000000000000−2i22i22i2−2i20000000000000000000
χ534-4-44-4-444000-444-40000000004i−4i000000000000000000000000000000000
χ544-4-44-4-444000-444-4000000000−4i4i000000000000000000000000000000000
χ554-4-4-4444-400000000002i2−2i2−2i22i2000000002i2−2i2000000002-2-22000000000000000
χ564-4-4-4444-400000000002i2−2i2−2i22i200000000−2i22i200000000-222-2000000000000000
χ574-4-4-4444-40000000000−2i22i22i2−2i2000000002i2−2i200000000-222-2000000000000000
χ584-4-4-4444-40000000000−2i22i22i2−2i200000000−2i22i2000000002-2-22000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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