Finite Group Databasebeta

← Group #337367

Character table — Group #337367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-11-1-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ4111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-11-11111-1-1-1-1-1
χ51111111111111111111111-1-111111111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-111111-11
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1111-11-1-111-1-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-111-1-111-111
χ13111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-111
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-111-1-111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1111-1-1-111111-1-1
χ1722222222222-2-2-2-22-2-22222220000000000-2-2000000002-200-20000000000
χ1822222222222-2-2-2-22-2-22222-2-20000000000-2-200000000-220020000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-22200000000002200000000-2-20020000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2000000000022000000002200-20000000000
χ2122222222-2-2-22222-2-2-200000022-2-22222-2-2000000000000000-2000000000
χ2222222222-2-2-22222-2-2-200000022-2-2-2-2-2-2220000000000000002000000000
χ2322222222-2-2-22222-2-2-2000000-2-22222-2-222000000000000000-2000000000
χ2422222222-2-2-22222-2-2-2000000-2-222-2-222-2-20000000000000002000000000
χ252-22-222-2-2-2-2222-2-222-200000000000000000022-2-20000002i−2i00002i−2i00000
χ262-22-222-2-2-2-2222-2-222-200000000000000000022-2-2000000−2i2i0000−2i2i00000
χ272-22-222-2-2-2-2222-2-222-2000000000000000000-2-2220000002i−2i0000−2i2i00000
χ282-22-222-2-2-2-2222-2-222-2000000000000000000-2-222000000−2i2i00002i−2i00000
χ292-2-222-22-20002-22-2000i2i2−i2−i200002-22-2002-2i2−i2i2−i2i2−i2i2i2−i2−i20000000000i2−i2000
χ302-2-222-22-20002-22-2000i2i2−i2−i200002-2-2200-22i2−i2i2−i2i2−i2−i2−i2i2i20000000000−i2i2000
χ312-2-222-22-20002-22-2000i2i2−i2−i20000-222-200-22i2−i2−i2i2−i2i2−i2−i2i2i20000000000i2−i2000
χ322-2-222-22-20002-22-2000i2i2−i2−i20000-22-22002-2i2−i2−i2i2−i2i2i2i2−i2−i20000000000−i2i2000
χ332-2-222-22-20002-22-2000−i2−i2i2i200002-22-2002-2−i2i2−i2i2−i2i2−i2−i2i2i20000000000−i2i2000
χ342-2-222-22-20002-22-2000−i2−i2i2i200002-2-2200-22−i2i2−i2i2−i2i2i2i2−i2−i20000000000i2−i2000
χ352-2-222-22-20002-22-2000−i2−i2i2i20000-222-200-22−i2i2i2−i2i2−i2i2i2−i2−i20000000000−i2i2000
χ362-2-222-22-20002-22-2000−i2−i2i2i20000-22-22002-2−i2i2i2−i2i2−i2−i2−i2i2i20000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ3844-44-44-4-44-440000-4004-44-40000000000000000000000000000000000000
χ3944-44-44-4-44-440000-400-44-440000000000000000000000000000000000000
χ4044-44-44-4-4-44-4000040000000000000000000000002i2−2i22i2−2i2000000000000000
χ4144-44-44-4-4-44-400004000000000000000000000000−2i22i2−2i22i2000000000000000
χ4244-4-44-4-440004-4-440000000000000000000002i2−2i2−2i22i20000000000000000000
χ4344-4-44-4-440004-4-44000000000000000000000−2i22i22i2−2i20000000000000000000
χ4444-4-44-4-44000-444-40000000004i−4i000000000000000000000000000000000
χ4544-4-44-4-44000-444-4000000000−4i4i000000000000000000000000000000000
χ464-444-4-4-4400000000002i2−2i2−2i22i2000000002i2−2i2000000002-2-22000000000000000
χ474-444-4-4-4400000000002i2−2i2−2i22i200000000−2i22i200000000-222-2000000000000000
χ484-444-4-4-440000000000−2i22i22i2−2i2000000002i2−2i200000000-222-2000000000000000
χ494-444-4-4-440000000000−2i22i22i2−2i200000000−2i22i2000000002-2-22000000000000000
χ504-44-444-4-444-444-4-4-4-4400000000000000000000000000000000000000000
χ514-44-444-4-444-4-4-444-44-400000000000000000000000000000000000000000
χ524-44-444-4-4-4-44-4-4444-4400000000000000000000000000000000000000000
χ534-4-444-44-4000-44-440002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ544-4-444-44-4000-44-44000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ554-4-4-4-44444-4-4000040000004-400000000000000000000000000000000000
χ564-4-4-4-44444-4-400004000000-4400000000000000000000000000000000000
χ574-4-4-4-4444-4440000-400000000000000000000000000000000002i2−2i20000000
χ584-4-4-4-4444-4440000-40000000000000000000000000000000000−2i22i20000000
χ59888-8-8-88-8000000000000000000000000000000000000000000000000000

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