Finite Group Databasebeta

← Group #315207

Character table — Group #315207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444444444444444444441616161616161616161616161616161632323232
order12222222444444444488888888888888888888888844444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-11-11-11-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-11-11-11-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-11-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-11111-111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111111-1-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1111-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111-111-1-1-1-111-1-1-11-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-111-11-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-11-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-11111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-11-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111-111-1-111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-11111-1-1-1-11111-1-1
χ172222222222-2-22-2-22-2-2000000002222-2-2-2-20000000020-20-2020000000000000
χ182222222222-2-22-2-22-2-2000000002222-2-2-2-200000000-202020-20000000000000
χ192222222222-2-22-2-22-2-200000000-2-2-2-222220000000020-2020-20000000000000
χ202222222222-2-22-2-22-2-200000000-2-2-2-2222200000000-2020-2020000000000000
χ2122222222-2-222-222-2-2-22222-2-2-2-2000000000000000002020-20-2000000000000
χ2222222222-2-222-222-2-2-22222-2-2-2-200000000000000000-20-20202000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-222220000000000000000020-20-202000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2222200000000000000000-202020-2000000000000
χ2522-22-2-22-22-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22i−2i0000
χ2622-22-2-22-22-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22−2i2i0000
χ2722-22-2-22-22-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-2−2i2i0000
χ2822-22-2-22-22-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-222i−2i0000
χ2922-22-2-22-2-2222-2-2-22-220000000022-2-222-2-200000000000000002i−2i2i−2i00000000
χ3022-22-2-22-2-2222-2-2-22-220000000022-2-222-2-20000000000000000−2i2i−2i2i00000000
χ3122-22-2-22-2-2222-2-2-22-2200000000-2-222-2-22200000000000000002i−2i−2i2i00000000
χ3222-22-2-22-2-2222-2-2-22-2200000000-2-222-2-2220000000000000000−2i2i2i−2i00000000
χ3322-22-2-22-2-22-2-2-22222-22i2i−2i−2i−2i−2i2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000
χ3422-22-2-22-2-22-2-2-22222-22i2i−2i−2i−2i−2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ3522-22-2-22-2-22-2-2-22222-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ3622-22-2-22-2-22-2-2-22222-2−2i−2i2i2i2i2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-44-4-44400-400-40000000000000000002222−22−222222−22−2200000000000000000000
χ39444-4-44-4-44400-400-4000000000000000000−22−222222−22−22222200000000000000000000
χ40444-4-44-4-4-4-400400400000000004i−4i4i−4i00000000000000000000000000000000
χ41444-4-44-4-4-4-40040040000000000−4i4i−4i4i00000000000000000000000000000000
χ4244-44-4-44-44-4444-4-4-44-400000000000000000000000000000000000000000000
χ4344-4-44-4-444-400-400400000000004i−4i−4i4i00000000000000000000000000000000
χ4444-4-44-4-444-400-40040000000000−4i4i4i−4i00000000000000000000000000000000
χ4544-4-44-4-44-4400400-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000
χ4644-4-44-4-44-4400400-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000
χ474-444-4-4-440000000000000022−2222−2200002i2−2i22i2−2i22i−2i2i−2i2i−2i2i−2i00000000000000000000
χ484-444-4-4-440000000000000022−2222−220000−2i22i2−2i22i2−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ494-444-4-4-4400000000000000−2222−222200002i2−2i22i2−2i2−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ504-444-4-4-4400000000000000−2222−22220000−2i22i2−2i22i22i−2i2i−2i2i−2i2i−2i00000000000000000000
χ514-44-44-44-4004-404-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000
χ524-44-44-44-4004-404-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000
χ534-44-44-44-400-440-440004i−4i4i−4i0000000000000000000000000000000000000000
χ544-44-44-44-400-440-44000−4i4i−4i4i0000000000000000000000000000000000000000
χ554-4-4444-4-4000000000000002i2−2i2−2i22i200002i2−2i2−2i22i2-22-222-22-200000000000000000000
χ564-4-4444-4-4000000000000002i2−2i2−2i22i20000−2i22i22i2−2i22-22-2-22-2200000000000000000000
χ574-4-4444-4-400000000000000−2i22i22i2−2i200002i2−2i2−2i22i22-22-2-22-2200000000000000000000
χ584-4-4444-4-400000000000000−2i22i22i2−2i20000−2i22i22i2−2i2-22-222-22-200000000000000000000
χ594-4-4-4-4444004-40-440004-4-440000000000000000000000000000000000000000
χ604-4-4-4-4444004-40-44000-444-40000000000000000000000000000000000000000
χ614-4-4-4-444400-4404-4000000000000000000022−22−2222−222222−2200000000000000000000
χ624-4-4-4-444400-4404-40000000000000000000−222222−2222−22−222200000000000000000000

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