Finite Group Databasebeta

← Group #72286536

Character table — Group #72286536

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222222444444888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222244442244442222444444422224444444444444444444488888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ511111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ9111-1-11-1-11-11-111111-1-111-11-1-1-11-11-11-11-1iiii−i−i−i−i11-1-1ii−i−i1-11-11-1ii−i−iii−i−i
χ10111-1-11-1-11-11-111111-1-111-11-1-1-11-11-11-11-1−i−i−i−iiiii11-1-1−i−iii1-11-11-1−i−iii−i−iii
χ11111-1-11-1-11-11-111111-1-111-11-1-1-11-1-111-1-11iiii−i−i−i−i-1-111ii−i−i-111-1-11−i−iii−i−iii
χ12111-1-11-1-11-11-111111-1-111-11-1-1-11-1-111-1-11−i−i−i−iiiii-1-111−i−iii-111-1-11ii−i−iii−i−i
χ13111-1-11-1-11-11-111111-1-111-11-1-1-1-111-1-111-1iiii−i−i−i−i-1-111−i−iii-11-111-1ii−i−i−i−iii
χ14111-1-11-1-11-11-111111-1-111-11-1-1-1-111-1-111-1−i−i−i−iiiii-1-111ii−i−i-11-111-1−i−iiiii−i−i
χ15111-1-11-1-11-11-111111-1-111-11-1-1-1-11-11-11-11iiii−i−i−i−i11-1-1−i−iii1-1-11-11−i−iiiii−i−i
χ16111-1-11-1-11-11-111111-1-111-11-1-1-1-11-11-11-11−i−i−i−iiiii11-1-1ii−i−i1-1-11-11ii−i−i−i−iii
χ17222222222222222-2-2-2-2-2-2-222-22000000000000000022220000-2-2000000000000
χ18222222222222222-2-2-2-2-2-2-222-220000000000000000-2-2-2-2000022000000000000
χ19222222222222-2-222-22-22-2-2-2-22-20022002200000000000000000000-2-200000000
χ20222222222222-2-222-22-22-2-2-2-22-200-2-200-2-2000000000000000000002200000000
χ21222222222222-2-22-22-22-222-2-2-2-222002200000000000000000000-2-20000000000
χ22222222222222-2-22-22-22-222-2-2-2-2-2-200-2-200000000000000000000220000000000
χ2322222-2-2-2-2-2-222222-22-2-222-22-2-200000000000000000000000000000000002i−2i2i−2i
χ2422222-2-2-2-2-2-222222-22-2-222-22-2-20000000000000000000000000000000000−2i2i−2i2i
χ2522222-2-2-2-2-2-22222-22-222-2-2-222-20000000022-2-222-2-20000000000000000000000
χ2622222-2-2-2-2-2-22222-22-222-2-2-222-200000000-2-222-2-2220000000000000000000000
χ2722222-2-2-2-2-2-22-2-222222-2-2-22-2-22000000000000000000002-22-200000000000000
χ2822222-2-2-2-2-2-22-2-222222-2-2-22-2-2200000000000000000000-22-2200000000000000
χ2922222-2-2-2-2-2-22-2-22-2-2-2-22222-2220000000000000000000000000000002-22-20000
χ3022222-2-2-2-2-2-22-2-22-2-2-2-22222-222000000000000000000000000000000-22-220000
χ31222-2-22-2-22-22-2222-2-222-2-222-22-2000000000000000022-2-20000-22000000000000
χ32222-2-22-2-22-22-2222-2-222-2-222-22-20000000000000000-2-22200002-2000000000000
χ33222-2-22-2-22-22-2-2-222-2-222-22-22-22002-2002-200000000000000000000-2200000000
χ34222-2-22-2-22-22-2-2-222-2-222-22-22-2200-2200-22000000000000000000002-200000000
χ35222-2-22-2-22-22-2-2-22-222-2-22-2-22222-2002-200000000000000000000-220000000000
χ36222-2-22-2-22-22-2-2-22-222-2-22-2-2222-2200-22000000000000000000002-20000000000
χ37222-2-2-222-22-2-22222-2-22-22-2-2-22200000000000000000000000000000000002-2-22
χ38222-2-2-222-22-2-22222-2-22-22-2-2-2220000000000000000000000000000000000-222-2
χ39222-2-2-222-22-2-2222-222-22-22-2-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ40222-2-2-222-22-2-2222-222-22-22-2-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ41222-2-2-222-22-2-2-2-2222-2-2-2-22222-2000000000000000000002i−2i−2i2i00000000000000
χ42222-2-2-222-22-2-2-2-2222-2-2-2-22222-200000000000000000000−2i2i2i−2i00000000000000
χ43222-2-2-222-22-2-2-2-22-2-22222-222-2-20000000000000000000000000000002i−2i−2i2i0000
χ44222-2-2-222-22-2-2-2-22-2-22222-222-2-2000000000000000000000000000000−2i2i2i−2i0000
χ45444444444-4-4-400-400000000000000000002-22-22-22-20000000000000000000000
χ46444444444-4-4-400-40000000000000000000-22-22-22-220000000000000000000000
χ4744444-4-4-4-444-400-400000000000000000002-2-222-2-220000000000000000000000
χ4844444-4-4-4-444-400-40000000000000000000-222-2-222-20000000000000000000000
χ49444-4-44-4-444-4400-400000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ50444-4-44-4-444-4400-40000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ51444-4-4-444-4-44400-400000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ52444-4-4-444-4-44400-40000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ5344-44-4-44-4400000000000000000222-2-2-2-22000000002-22-2000000000000000000
χ5444-44-4-44-440000000000000000022-22-2-22-200000000-22-22000000000000000000
χ5544-44-4-44-4400000000000000000-2-22-222-2200000000-22-22000000000000000000
χ5644-44-4-44-4400000000000000000-2-2-22222-2000000002-22-2000000000000000000
χ5744-4-44-4-444000000000000000002-222-22-2-2000000002-2-22000000000000000000
χ5844-4-44-4-444000000000000000002-2-2-2-222200000000-222-2000000000000000000
χ5944-4-44-4-44400000000000000000-22222-2-2-200000000-222-2000000000000000000
χ6044-4-44-4-44400000000000000000-22-2-22-222000000002-2-22000000000000000000
χ6188-88-88-88-80000000000000000000000000000000000000000000000000000000
χ6288-8-8888-8-80000000000000000000000000000000000000000000000000000000
χ6316-1600000000008i−8i00000000000000000000000000000000000000000000000000
χ6416-160000000000−8i8i00000000000000000000000000000000000000000000000000

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