Finite Group Databasebeta

← Group #72287675

Character table — Group #72287675

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1122222224444444444444488888888888161616161616323232323232323232323232323232323232323232323232
order122448888244444444488882488888161616161616161616168888888816161616161616163232323232323232
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111-1-111-1-1111111-1-11-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-111-1-1111111-1-11-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111-1-111-1-1111111-1-11-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111-1-111-1-1111111-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111-1-11111-1-1-1-1-1-1-11-1-11-1111-1-11111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111111-1-11111-1-1-1-1-1-1-11-1-11-1111-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111111-1-11111-1-1-1-1-1-1-11-1-11-1111-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111111-1-11111-1-1-1-1-1-1-11-1-11-1111-1-11111-1-1-1-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111111-1-111-1-1-1-111-1-1-11-1-1-111-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111111-1-111-1-1-1-111-1-1-11-1-1-111-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111111-1-111-1-1-1-111-1-1-11-1-1-111-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111111-1-111-1-1-1-111-1-1-11-1-1-111-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222-2-222-2-2222222-2-22-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222-2-2002200-2-222-2-200-2000022-2-2002-20000002i−2i2i−2i0000000000000000
χ20222222222-2-2002200-2-222-2-200-2000022-2-2002-2000000−2i2i−2i2i0000000000000000
χ21222222222-2-2002200-2-222-2-200-20000-2-22200-22002i−2i2i−2i00000000000000000000
χ22222222222-2-2002200-2-222-2-200-20000-2-22200-2200−2i2i−2i2i00000000000000000000
χ232222222-2-22222-2-2-2-2-2-2-22-2-22-2222-2-2-2-2-2-22222-2-2000000000000000000000000
χ242222222-2-222-2-2-2-222-2-2-22-2-2-222-2-222-2-2-2-2-2-22222000000000000000000000000
χ252222222-2-2-2-200-2-20022-222200-2000022-2-200-220000002-2-220000000000000000
χ262222222-2-2-2-200-2-20022-222200-2000022-2-200-22000000-222-20000000000000000
χ272222222-2-2-2-200-2-20022-222200-20000-2-222002-2002-2-2200000000000000000000
χ282222222-2-2-2-200-2-20022-222200-20000-2-222002-200-222-200000000000000000000
χ2922222-2-2222222-2-2-2-2-2-22-2222-2-2-2-22200000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ3022222-2-2222222-2-2-2-2-2-22-2222-2-2-2-22200000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ3122222-2-22222-2-2-2-222-2-22-222-22-222-2-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ3222222-2-22222-2-2-2-222-2-22-222-22-222-2-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ3322222-2-2-2-22222222222-2-2-2-222-2-2-2-2-200000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3422222-2-2-2-22222222222-2-2-2-222-2-2-2-2-200000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3522222-2-2-2-222-2-222-2-222-2-2-2-2-2-2-2222200000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ3622222-2-2-2-222-2-222-2-222-2-2-2-2-2-2-2222200000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3744444-4-444-4-400-4-400444-4-4-400400000000000000000000000000000000000000
χ3844444-4-4-4-4-4-4004400-4-4-4-44400400000000000000000000000000000000000000
χ39444-4-400004-4440000000000-40000002i2−2i22i2−2i200002i2−2i2000000000000000000000000
χ40444-4-400004-4440000000000-4000000−2i22i2−2i22i20000−2i22i2000000000000000000000000
χ41444-4-400004-4-4-4000000000040000002i2−2i22i2−2i20000−2i22i2000000000000000000000000
χ42444-4-400004-4-4-400000000004000000−2i22i2−2i22i200002i2−2i2000000000000000000000000
χ43444-4-40000-440000440000000-4000002i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ44444-4-40000-440000440000000-400000−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ45444-4-40000-440000-4-400000004000002i2−2i2−2i22i2−2i22i20000000000000000000000000000
χ46444-4-40000-440000-4-40000000400000−2i22i22i2−2i22i2−2i20000000000000000000000000000
χ4744-44-44400000000004i−4i0-44i−4i000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4844-44-44400000000004i−4i0-44i−4i00000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4944-44-4440000000000−4i4i0-4−4i4i000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ5044-44-4440000000000−4i4i0-4−4i4i00000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ5144-44-4-4-400000000004i−4i04−4i4i00000000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ5244-44-4-4-400000000004i−4i04−4i4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ5344-44-4-4-40000000000−4i4i044i−4i00000000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ5444-44-4-4-40000000000−4i4i044i−4i0000000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ5588-8-8800880000000000-800000000000000000000000000000000000000000000
χ5688-8-8800-8-80000000000800000000000000000000000000000000000000000000
χ578-80004i2−4i242−42004i−4i4i−4i4-400000000022−222i2−2i20000000000000000000000000000000000
χ588-80004i2−4i242−4200−4i4i4i−4i-44000000000−2222−2i22i20000000000000000000000000000000000
χ598-80004i2−4i2−4242004i−4i−4i4i-4400000000022−22−2i22i20000000000000000000000000000000000
χ608-80004i2−4i2−424200−4i4i−4i4i4-4000000000−22222i2−2i20000000000000000000000000000000000
χ618-8000−4i24i242−42004i−4i−4i4i-44000000000−22222i2−2i20000000000000000000000000000000000
χ628-8000−4i24i242−4200−4i4i−4i4i4-400000000022−22−2i22i20000000000000000000000000000000000
χ638-8000−4i24i2−4242004i−4i4i−4i4-4000000000−2222−2i22i20000000000000000000000000000000000
χ648-8000−4i24i2−424200−4i4i4i−4i-4400000000022−222i2−2i20000000000000000000000000000000000

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