Finite Group Databasebeta

← Group #337162

Character table — Group #337162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111111111111-1-1-11-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-11-1-1
χ51111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-111
χ71111111111111111111111-1-1-1-111-1-1111111-1-1-1-111111-1-1-1111111-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1111-1111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-111-1-11-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111111-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-11-1-111-1-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-111-111-1-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-1-1-11111-11-1
χ172222222222-2-22-2-22-2-2222200002200-2-20000000000002000-2-2000000000
χ182222222222-2-22-2-22-2-222220000-2-200-2-2000000000000-200022000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000220022000000000000-20002-2000000000
χ202222222222-2-22-2-22-2-2-2-2-2-20000-2-200220000000000002000-22000000000
χ2122222222-2-222-222-2-2-20000222200-2-20022-2-200000000000-200000000000
χ2222222222-2-222-222-2-2-2000022-2-200-2-200-2-22200000000000200000000000
χ2322222222-2-222-222-2-2-20000-2-222002200-2-22200000000000-200000000000
χ2422222222-2-222-222-2-2-20000-2-2-2-200220022-2-200000000000200000000000
χ2522-22-2-2-22-2-2222-2-222-200000000000000000022-2-2000002i−2i000002i−2i00000
χ2622-22-2-2-22-2-2222-2-222-200000000000000000022-2-200000−2i2i00000−2i2i00000
χ2722-22-2-2-22-2-2222-2-222-2000000000000000000-2-222000002i−2i00000−2i2i00000
χ2822-22-2-2-22-2-2222-2-222-2000000000000000000-2-22200000−2i2i000002i−2i00000
χ2922-2-2-222-2002-202-2000i2i2−i2−i2002i−2i002i−2ii2−i2002-22−22−2i2i2−i2−i200000000002−2000
χ3022-2-2-222-2002-202-2000i2i2−i2−i2002i−2i00−2i2ii2−i200-22−22−22−i2−i2i2i200000000002−2000
χ3122-2-2-222-2002-202-2000i2i2−i2−i200−2i2i002i−2ii2−i200-222−22−2−i2−i2i2i20000000000−22000
χ3222-2-2-222-2002-202-2000i2i2−i2−i200−2i2i00−2i2ii2−i2002-2−22−22i2i2−i2−i20000000000−22000
χ3322-2-2-222-2002-202-2000−i2−i2i2i2002i−2i002i−2i−i2i2002-2−22−22−i2−i2i2i20000000000−22000
χ3422-2-2-222-2002-202-2000−i2−i2i2i2002i−2i00−2i2i−i2i200-222−22−2i2i2−i2−i20000000000−22000
χ3522-2-2-222-2002-202-2000−i2−i2i2i200−2i2i002i−2i−i2i200-22−22−22i2i2−i2−i200000000002−2000
χ3622-2-2-222-2002-202-2000−i2−i2i2i200−2i2i00−2i2i−i2i2002-22−22−2−i2−i2i2i200000000002−2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-44-4-4-4004-40-4400000000000000000000022−22−22220000000000000000000
χ39444-44-4-4-4004-40-44000000000000000000000−222222−220000000000000000000
χ40444-44-4-4-400-4404-400000004-400000000000000000000000000000000000
χ41444-44-4-4-400-4404-40000000-4400000000000000000000000000000000000
χ4244-44-4-4-444444-4-4-4-4-4400000000000000000000000000000000000000000
χ4344-44-4-4-4444-4-4-444-44-400000000000000000000000000000000000000000
χ4444-44-4-4-44-4-4-4-44444-4400000000000000000000000000000000000000000
χ4544-4-4-444-400-440-440002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ4644-4-4-444-400-440-44000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ474-44-4-4-4444-400400-40000000000000000000000002i2−2i22i2−2i2000000000000000
χ484-44-4-4-4444-400400-4000000000000000000000000−2i22i2−2i22i2000000000000000
χ494-44-4-4-444-4400-4004004-44-40000000000000000000000000000000000000
χ504-44-4-4-444-4400-400400-44-440000000000000000000000000000000000000
χ514-4-444-44-400000000002i2−2i2−2i22i200000000002i2−2i20000002-2-22000000000000000
χ524-4-444-44-400000000002i2−2i2−2i22i20000000000−2i22i2000000-222-2000000000000000
χ534-4-444-44-40000000000−2i22i22i2−2i200000000002i2−2i2000000-222-2000000000000000
χ544-4-444-44-40000000000−2i22i22i2−2i20000000000−2i22i20000002-2-22000000000000000
χ554-4-4-444-444-400-4004000000000000000000000000000000000022−220000000
χ564-4-4-444-444-400-40040000000000000000000000000000000000−22220000000
χ574-4-4-444-44-4400400-400000000004i−4i0000000000000000000000000000000
χ584-4-4-444-44-4400400-40000000000−4i4i0000000000000000000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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