Finite Group Databasebeta

← Group #337184

Character table — Group #337184

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1
χ4111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-11111-1-1-1-1-1
χ51111111111111111111111-1-111111111111111111111-1-1-11-1-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1111111-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-111-1-1111-11
χ13111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11-11
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-11-11111-1-111-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-111-1-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-111-1-11111-11-1
χ172222222222-2-2-2-222-2-22222220000000000-2-2000000002-2-2000000000000
χ182222222222-2-2-2-222-2-22222-2-20000000000-2-200000000-222000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-22200000000002200000000-2-22000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-20000000000220000000022-2000000000000
χ2122222222-2-22222-2-2-2-20000002222-2-222-2-20000000000000-200000000000
χ2222222222-2-22222-2-2-2-200000022-2-2-2-2-2-2220000000000000200000000000
χ2322222222-2-22222-2-2-2-2000000-2-22222-2-2220000000000000-200000000000
χ2422222222-2-22222-2-2-2-2000000-2-2-2-22222-2-20000000000000200000000000
χ2522-2-2-2-222002-22-20000i2i2−i2−i200002i−2i2-2002i−2ii2−i2i2i2−i2−i222−2−200000000002−2000
χ2622-2-2-2-222002-22-20000i2i2−i2−i200002i−2i-2200−2i2ii2−i2−i2−i2i2i2−2−22200000000002−2000
χ2722-2-2-2-222002-22-20000i2i2−i2−i20000−2i2i2-200−2i2ii2−i2i2i2−i2−i2−2−2220000000000−22000
χ2822-2-2-2-222002-22-20000i2i2−i2−i20000−2i2i-22002i−2ii2−i2−i2−i2i2i222−2−20000000000−22000
χ2922-2-2-2-222002-22-20000−i2−i2i2i200002i−2i2-2002i−2i−i2i2−i2−i2i2i2−2−2220000000000−22000
χ3022-2-2-2-222002-22-20000−i2−i2i2i200002i−2i-2200−2i2i−i2i2i2i2−i2−i222−2−20000000000−22000
χ3122-2-2-2-222002-22-20000−i2−i2i2i20000−2i2i2-200−2i2i−i2i2−i2−i2i2i222−2−200000000002−2000
χ3222-2-2-2-222002-22-20000−i2−i2i2i20000−2i2i-22002i−2i−i2i2i2i2−i2−i2−2−22200000000002−2000
χ332-22-22-22-2-2-222-2-2222-20000000000000000002-22-2000000002i−2i002i−2i00000
χ342-22-22-22-2-2-222-2-2222-20000000000000000002-22-200000000−2i2i00−2i2i00000
χ352-22-22-22-2-2-222-2-2222-2000000000000000000-22-22000000002i−2i00−2i2i00000
χ362-22-22-22-2-2-222-2-2222-2000000000000000000-22-2200000000−2i2i002i−2i00000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-44-400004-40000004-400000000000000000000000000000000000
χ394444-4-4-4-44-400004-4000000-4400000000000000000000000000000000000
χ404444-4-4-4-4-440000-44000000000000000000000000000000000022−220000000
χ414444-4-4-4-4-440000-440000000000000000000000000000000000−22220000000
χ4244-4-4-4-44400-44-4400002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ4344-4-4-4-44400-44-440000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ444-44-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ454-44-44-44-444-4-444-4-44-400000000000000000000000000000000000000000
χ464-44-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ474-44-4-44-444-40000-44004i−4i4i−4i0000000000000000000000000000000000000
χ484-44-4-44-444-40000-4400−4i4i−4i4i0000000000000000000000000000000000000
χ494-44-4-44-44-4400004-40000000000000000000000002i2−2i22i2−2i2000000000000000
χ504-44-4-44-44-4400004-4000000000000000000000000−2i22i2−2i22i2000000000000000
χ514-4-444-4-44000000000022−22−2222000000002i2−2i2000000002i−2i−2i2i000000000000000
χ524-4-444-4-44000000000022−22−222200000000−2i22i200000000−2i2i2i−2i000000000000000
χ534-4-444-4-440000000000−222222−22000000002i2−2i200000000−2i2i2i−2i000000000000000
χ544-4-444-4-440000000000−222222−2200000000−2i22i2000000002i−2i−2i2i000000000000000
χ554-4-44-444-4004-4-4400000000000000000000002i2−2i2−2i22i20000000000000000000
χ564-4-44-444-4004-4-440000000000000000000000−2i22i22i2−2i20000000000000000000
χ574-4-44-444-400-444-400000000004i−4i000000000000000000000000000000000
χ584-4-44-444-400-444-40000000000−4i4i000000000000000000000000000000000
χ5988-8-888-8-8000000000000000000000000000000000000000000000000000

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