Finite Group Databasebeta

← Group #337268

Character table — Group #337268

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1
χ4111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1-11111-1-1-1
χ51111111111111111111111-1-111111111111111111111-1-1-11-1-111-1-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-11-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11-1-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-11111-1-1-111
χ13111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-111
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-1111111-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11111-1-1111-1-1
χ172222222222-2-2-222-2-2-22222220000000000-2-200000000-22-2000000000000
χ182222222222-2-2-222-2-2-22222-2-20000000000-2-2000000002-22000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-22200000000002200000000-2-22000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-20000000000220000000022-2000000000000
χ2122222222-2-2222-2-22-2-20000002222-2-222-2-20000000000000-200000000000
χ2222222222-2-2222-2-22-2-200000022-2-2-2-2-2-2220000000000000200000000000
χ2322222222-2-2222-2-22-2-2000000-2-22222-2-2220000000000000-200000000000
χ2422222222-2-2222-2-22-2-2000000-2-2-2-22222-2-20000000000000200000000000
χ2522-2-22-22-200-22-20020022−2−2002i−2i2-2002i−2i002−2i2i2−i2−i2i2i2−i2−i20000002−20000000
χ2622-2-22-22-200-22-20020022−2−2002i−2i-2200−2i2i002−2i2i2−i2−i2−i2−i2i2i2000000−220000000
χ2722-2-22-22-200-22-20020022−2−200−2i2i2-200−2i2i002−2−i2−i2i2i2−i2−i2i2i20000002−20000000
χ2822-2-22-22-200-22-20020022−2−200−2i2i-22002i−2i002−2−i2−i2i2i2i2i2−i2−i2000000−220000000
χ2922-2-22-22-200-22-200200−2−222002i−2i2-2002i−2i00−22−i2−i2i2i2−i2−i2i2i2000000−220000000
χ3022-2-22-22-200-22-200200−2−222002i−2i-2200−2i2i00−22−i2−i2i2i2i2i2−i2−i20000002−20000000
χ3122-2-22-22-200-22-200200−2−22200−2i2i2-200−2i2i00−22i2i2−i2−i2i2i2−i2−i2000000−220000000
χ3222-2-22-22-200-22-200200−2−22200−2i2i-22002i−2i00−22i2i2−i2−i2−i2−i2i2i20000002−20000000
χ332-222-2-22-2-2-2-22222-22-20000000000000000002-22-2000000002i−2i00002i−2i000
χ342-222-2-22-2-2-2-22222-22-20000000000000000002-22-200000000−2i2i0000−2i2i000
χ352-222-2-22-2-2-2-22222-22-2000000000000000000-22-22000000002i−2i0000−2i2i000
χ362-222-2-22-2-2-2-22222-22-2000000000000000000-22-2200000000−2i2i00002i−2i000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-44-40004-400000004-400000000000000000000000000000000000
χ39444-4-44-4-44-40004-40000000-4400000000000000000000000000000000000
χ40444-4-44-4-4-44000-44000000000000000000000000000000000000022−2200000
χ41444-4-44-4-4-44000-440000000000000000000000000000000000000−222200000
χ4244-4-44-44-4004-4400-4002222−22−22000000000000−222200000000000000000000000
χ4344-4-44-44-4004-4400-400−22−22222200000000000022−2200000000000000000000000
χ444-444-4-44-4444-4-4-4-444-400000000000000000000000000000000000000000
χ454-444-4-44-444-444-4-4-4-4400000000000000000000000000000000000000000
χ464-444-4-44-4-4-44-4-4444-4400000000000000000000000000000000000000000
χ474-44-44-4-444-4000-440004i−4i4i−4i0000000000000000000000000000000000000
χ484-44-44-4-444-4000-44000−4i4i−4i4i0000000000000000000000000000000000000
χ494-44-44-4-44-440004-400000000000000000000000002i2−2i22i2−2i2000000000000000
χ504-44-44-4-44-440004-40000000000000000000000000−2i22i2−2i22i2000000000000000
χ514-4-4444-4-400000000002i2−2i2−2i22i200000000002i2−2i20000002-2-22000000000000000
χ524-4-4444-4-400000000002i2−2i2−2i22i20000000000−2i22i2000000-222-2000000000000000
χ534-4-4444-4-40000000000−2i22i22i2−2i200000000002i2−2i2000000-222-2000000000000000
χ544-4-4444-4-40000000000−2i22i22i2−2i20000000000−2i22i20000002-2-22000000000000000
χ554-4-4-4-44440044-400-4000000000000000000002i2−2i2−2i22i20000000000000000000
χ564-4-4-4-44440044-400-400000000000000000000−2i22i22i2−2i20000000000000000000
χ574-4-4-4-444400-4-440040000000000004-400000000000000000000000000000
χ584-4-4-4-444400-4-44004000000000000-4400000000000000000000000000000
χ5988-88-8-8-88000000000000000000000000000000000000000000000000000

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