Finite Group Databasebeta

← Group #337191

Character table — Group #337191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1
χ4111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1111-1-11111-1-1-1-1-1
χ51111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1111111-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-111-1-111-111
χ13111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-111
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-111-1-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111111-1-1
χ172222222222-22-2-2-22-2-22222220000000000-2-2000000000-2-2200000000000
χ182222222222-22-2-2-22-2-22222-2-20000000000-2-200000000022-200000000000
χ192222222222-22-2-2-22-2-2-2-2-2-222000000000022000000000-22-200000000000
χ202222222222-22-2-2-22-2-2-2-2-2-2-2-20000000000220000000002-2200000000000
χ2122222222-2-22-2222-2-2-200000022-2-22222-2-20000000000-200000000000000
χ2222222222-2-22-2222-2-2-200000022-2-2-2-2-2-2220000000000200000000000000
χ2322222222-2-22-2222-2-2-2000000-2-22222-2-2220000000000-200000000000000
χ2422222222-2-22-2222-2-2-2000000-2-222-2-222-2-20000000000200000000000000
χ2522-2-22-22-2-2-2-2222-222-200000000000000000022-2-2000000002i−2i002i−2i00000
χ2622-2-22-22-2-2-2-2222-222-200000000000000000022-2-200000000−2i2i00−2i2i00000
χ2722-2-22-22-2-2-2-2222-222-2000000000000000000-2-222000000002i−2i00−2i2i00000
χ2822-2-22-22-2-2-2-2222-222-2000000000000000000-2-22200000000−2i2i002i−2i00000
χ292-2-2-222-2200202-2-200022−2−200002i−2i2-2002i−2i2−2i2−i2i2−i2i2i2−i2−i200000000002−2000
χ302-2-2-222-2200202-2-200022−2−200002i−2i-2200−2i2i2−2i2−i2i2−i2−i2−i2i2i20000000000−22000
χ312-2-2-222-2200202-2-200022−2−20000−2i2i2-200−2i2i2−2−i2i2−i2i2−i2−i2i2i200000000002−2000
χ322-2-2-222-2200202-2-200022−2−20000−2i2i-22002i−2i2−2−i2i2−i2i2i2i2−i2−i20000000000−22000
χ332-2-2-222-2200202-2-2000−2−22200002i−2i2-2002i−2i−22−i2i2−i2i2−i2−i2i2i20000000000−22000
χ342-2-2-222-2200202-2-2000−2−22200002i−2i-2200−2i2i−22−i2i2−i2i2i2i2−i2−i200000000002−2000
χ352-2-2-222-2200202-2-2000−2−2220000−2i2i2-200−2i2i−22i2−i2i2−i2i2i2−i2−i20000000000−22000
χ362-2-2-222-2200202-2-2000−2−2220000−2i2i-22002i−2i−22i2−i2i2−i2−i2−i2i2i200000000002−2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-4-444-404000-40000004-400000000000000000000000000000000000
χ39444-4-4-4-444-404000-4000000-4400000000000000000000000000000000000
χ40444-4-4-4-44-440-4000400000000000000000000000000000000002i2−2i20000000
χ41444-4-4-4-44-440-400040000000000000000000000000000000000−2i22i20000000
χ4244-44-44-4-44-40-40004004i−4i4i−4i0000000000000000000000000000000000000
χ4344-44-44-4-44-40-4000400−4i4i−4i4i0000000000000000000000000000000000000
χ4444-44-44-4-4-4404000-400000000000000000000000022−2222−22000000000000000
χ4544-44-44-4-4-4404000-4000000000000000000000000−2222−2222000000000000000
χ4644-4-44-44-4444-4-4-44-44-400000000000000000000000000000000000000000
χ4744-4-44-44-444-4-444-4-4-4400000000000000000000000000000000000000000
χ4844-4-44-44-4-4-444-4-444-4400000000000000000000000000000000000000000
χ494-4444-4-4-40040-44-40000000004-4000000000000000000000000000000000
χ504-4444-4-4-40040-44-4000000000-44000000000000000000000000000000000
χ514-4444-4-4-400-404-440000000000000000000002i2−2i2−2i22i20000000000000000000
χ524-4444-4-4-400-404-44000000000000000000000−2i22i22i2−2i20000000000000000000
χ534-44-4-444-400000000002i2−2i2−2i22i20000000022−22000000002i−2i−2i2i000000000000000
χ544-44-4-444-400000000002i2−2i2−2i22i200000000−222200000000−2i2i2i−2i000000000000000
χ554-44-4-444-40000000000−2i22i22i2−2i20000000022−2200000000−2i2i2i−2i000000000000000
χ564-44-4-444-40000000000−2i22i22i2−2i200000000−2222000000002i−2i−2i2i000000000000000
χ574-4-4-444-4400-40-4440002222−22−22000000000000−222200000000000000000000000
χ584-4-4-444-4400-40-444000−22−22222200000000000022−2200000000000000000000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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