Finite Group Databasebeta

← Group #94367

Character table — Group #94367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224444444444444422448888888888888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11iiii−i−i−i−i1111-1-1-1-1
χ611111111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−i−i−iiiii-1-1-1-11111
χ711111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11iiii−i−i−i−i-1-1-1-11111
χ811111111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11−i−i−i−iiiii1111-1-1-1-1
χ91111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11ii−i−i−i−iii−i−iiiii−i−i
χ141111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11−i−iiiii−i−iii−i−i−i−iii
χ151111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii
χ161111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i
χ17222222222222222222222222-2-2-2-20000000000000000-2-20000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222220000000000000000-2-20000000000000000
χ192222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22200000000000000002-20000000000000000
χ202222-2-2-2-222-2-222-2-2-2-222-2-22222-2-200000000000000002-20000000000000000
χ2122-2-22i2i−2i−2i2-22i−2i2-20000002i−2i002-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000
χ2222-2-22i2i−2i−2i2-22i−2i2-20000002i−2i002-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000
χ2322-2-22i2i−2i−2i2-22i−2i2-20000002i−2i00-22−2i2i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i000000000000000000
χ2422-2-22i2i−2i−2i2-22i−2i2-20000002i−2i00-22−2i2i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i000000000000000000
χ2522-2-22i2i−2i−2i2-22i−2i-222i2i−2i−2i2-2−2i2i2-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ2622-2-22i2i−2i−2i2-22i−2i-222i2i−2i−2i2-2−2i2i2-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ2722-2-22i2i−2i−2i2-22i−2i-22−2i−2i2i2i-22−2i2i-2200000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ2822-2-22i2i−2i−2i2-22i−2i-22−2i−2i2i2i-22−2i2i-220000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ2922-2-2−2i−2i2i2i2-2−2i2i2-2000000−2i2i002-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000
χ3022-2-2−2i−2i2i2i2-2−2i2i2-2000000−2i2i002-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000
χ3122-2-2−2i−2i2i2i2-2−2i2i2-2000000−2i2i00-222i−2i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i000000000000000000
χ3222-2-2−2i−2i2i2i2-2−2i2i2-2000000−2i2i00-222i−2i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i000000000000000000
χ3322-2-2−2i−2i2i2i2-2−2i2i-222i2i−2i−2i-222i−2i-2200000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ3422-2-2−2i−2i2i2i2-2−2i2i-222i2i−2i−2i-222i−2i-220000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ3522-2-2−2i−2i2i2i2-2−2i2i-22−2i−2i2i2i2-22i−2i2-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ3622-2-2−2i−2i2i2i2-2−2i2i-22−2i−2i2i2i2-22i−2i2-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ37444444444444-4-4000000-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-40000000000000000000000000000000000000000002-22-20000
χ3944444444-4-4-4-4000000000000000000000000000000000000000000-22-220000
χ404444-4-4-4-444-4-4-4-4000000440000000000000000000000000000000000000000
χ414444-4-4-4-4-4-4440000000000000000000000000000000000000000002i−2i−2i2i0000
χ424444-4-4-4-4-4-444000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4344-4-44i4i−4i−4i-44−4i4i00000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4444-4-44i4i−4i−4i-44−4i4i0000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4544-4-4−4i−4i4i4i-444i−4i00000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4644-4-4−4i−4i4i4i-444i−4i0000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ474-44-44i−4i4i−4i0000002i−2i2i−2i2-200-2200002−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000000000
χ484-44-44i−4i4i−4i0000002i−2i2i−2i2-200-220000−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000000000
χ494-44-44i−4i4i−4i000000−2i2i−2i2i-22002-20000i2−i2i2−i2−22−222−22−2−i2i2−i2i2000000000000000000
χ504-44-44i−4i4i−4i000000−2i2i−2i2i-22002-20000−i2i2−i2i22−22−2−22−22i2−i2i2−i2000000000000000000
χ514-44-4−4i4i−4i4i0000002i−2i2i−2i-22002-20000i2−i2i2−i22−22−2−22−22−i2i2−i2i2000000000000000000
χ524-44-4−4i4i−4i4i0000002i−2i2i−2i-22002-20000−i2i2−i2i2−22−222−22−2i2−i2i2−i2000000000000000000
χ534-44-4−4i4i−4i4i000000−2i2i−2i2i2-200-2200002−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000000000
χ544-44-4−4i4i−4i4i000000−2i2i−2i2i2-200-220000−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000000000
χ554-4-444-4-440000002-2-222200-2-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ564-4-444-4-440000002-2-222200-2-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ574-4-444-4-44000000-222-2-2-2002200002−2−22−222−22−2−222−2−22000000000000000000
χ584-4-444-4-44000000-222-2-2-200220000−222−22−2−22−222−2−222−2000000000000000000
χ594-4-44-444-40000002-2-22-2-2002200002−2−222−2−22−222−22−2−22000000000000000000
χ604-4-44-444-40000002-2-22-2-200220000−222−2−222−22−2−22−222−2000000000000000000
χ614-4-44-444-4000000-222-22200-2-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ624-4-44-444-4000000-222-22200-2-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.