Finite Group Databasebeta

← Group #72319484

Character table — Group #72319484

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222222444444888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222222224444442222222244422224444444444448888444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ91111-1-1-1-111111-1-1111-1-1-11-11-1-1111-1-1-11-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i1-1i−iii−i−i
χ101111-1-1-1-111111-1-1111-1-1-11-11-1-1111-1-1-11-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii1-1−ii−i−iii
χ111111-1-1-1-111111-1-1111-1-1-11-11-1-111-11-1-1-11ii−i−i11-1-1−i−iii−ii-1-111ii−i−i-11i−i−i−iii
χ121111-1-1-1-111111-1-1111-1-1-11-11-1-111-11-1-1-11−i−iii11-1-1ii−i−ii−i-1-111−i−iii-11−iiii−i−i
χ131111-1-1-1-111111-1-1111-1-1-11-11-1-1-1-11-1111-1ii−i−i-1-111ii−i−ii−i-1-111−i−iii1-1i−i−i−iii
χ141111-1-1-1-111111-1-1111-1-1-11-11-1-1-1-11-1111-1−i−iii-1-111−i−iii−ii-1-111ii−i−i1-1−iiii−i−i
χ151111-1-1-1-111111-1-1111-1-1-11-11-1-1-1-1-1111-11ii−i−i-1-111−i−iii−ii11-1-1−i−iii-11i−iii−i−i
χ161111-1-1-1-111111-1-1111-1-1-11-11-1-1-1-1-1111-11−i−iii-1-111ii−i−ii−i11-1-1ii−i−i-11−ii−i−iii
χ17222222222222222-2-2-2-2-2-2-2-222200000000000000002222-2-20000000000000000
χ18222222222222222-2-2-2-2-2-2-2-22220000000000000000-2-2-2-2220000000000000000
χ192222222222-2-222222-22-2-2-22-2-2-200000000222200000000000000000000-2-20000
χ202222222222-2-222222-22-2-2-22-2-2-200000000-2-2-2-200000000000000000000220000
χ212222222222-2-2222-2-22-2222-2-2-2-2002200220000000000000000000000-2-2000000
χ222222222222-2-2222-2-22-2222-2-2-2-200-2-200-2-2000000000000000000000022000000
χ232222-2-2-2-222222-2-2-2-2-2222-222-2-200000000000000002i2i−2i−2i−2i2i0000000000000000
χ242222-2-2-2-222222-2-2-2-2-2222-222-2-20000000000000000−2i−2i2i2i2i−2i0000000000000000
χ252222-2-2-2-222-2-22-2-222-2-222-2-2-222000000002i2i−2i−2i00000000000000000000−2i2i0000
χ262222-2-2-2-222-2-22-2-222-2-222-2-2-22200000000−2i−2i2i2i000000000000000000002i−2i0000
χ272222-2-2-2-222-2-22-2-2-2-222-2-222-222002-2002-20000000000000000000000-22000000
χ282222-2-2-2-222-2-22-2-2-2-222-2-222-22200-2200-2200000000000000000000002-2000000
χ2922-2-22-22-22-22222-22-2222-2-2-2-22-2000000000000000000000000002i−2i2i−2i00000000
χ3022-2-22-22-22-22222-22-2222-2-2-2-22-200000000000000000000000000−2i2i−2i2i00000000
χ3122-2-22-22-22-22222-2-22-2-2-2222-22-200000000000000000000002-22-2000000000000
χ3222-2-22-22-22-22222-2-22-2-2-2222-22-20000000000000000000000-22-22000000000000
χ3322-2-22-22-22-2-2-222-22-2-22-222-22-222-2002-20000002-22-20000000000000000000000
χ3422-2-22-22-22-2-2-222-22-2-22-222-22-22-2200-22000000-22-220000000000000000000000
χ3522-2-22-22-22-2-2-222-2-222-22-2-222-2200000000000000000000000000000000002-22-2
χ3622-2-22-22-22-2-2-222-2-222-22-2-222-220000000000000000000000000000000000-22-22
χ3722-2-2-22-222-2222-222-22-2-22-22-2-22000000000000000000000000002-2-2200000000
χ3822-2-2-22-222-2222-222-22-2-22-22-2-2200000000000000000000000000-222-200000000
χ3922-2-2-22-222-2222-22-22-222-22-2-2-2200000000000000000000002-2-22000000000000
χ4022-2-2-22-222-2222-22-22-222-22-2-2-220000000000000000000000-222-2000000000000
χ4122-2-2-22-222-2-2-22-222-2-2-22-22222-22-200-220000002-2-220000000000000000000000
χ4222-2-2-22-222-2-2-22-222-2-2-22-22222-2-22002-2000000-222-20000000000000000000000
χ4322-2-2-22-222-2-2-22-22-2222-22-2-222-200000000000000000000000000000000002i−2i−2i2i
χ4422-2-2-22-222-2-2-22-22-2222-22-2-222-20000000000000000000000000000000000−2i2i2i−2i
χ45444444444-400-4-4-400000000000220022000000-2-2-2-20000000000000000000000
χ46444444444-400-4-4-400000000000-2-200-2-200000022220000000000000000000000
χ474444-4-4-4-44-400-444000000000002200-2-2000000-2-2220000000000000000000000
χ484444-4-4-4-44-400-44400000000000-2-2002200000022-2-20000000000000000000000
χ49444-444-4-4-400000000000000000002200-2-22i−2i2i−2i00002i−2i2i−2i000000000000000000
χ50444-444-4-4-400000000000000000002200-2-2−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ51444-444-4-4-40000000000000000000-2-200222i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ52444-444-4-4-40000000000000000000-2-20022−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ53444-4-4-444-400000000000000000002-200-222-2-2200002-2-22000000000000000000
χ54444-4-4-444-400000000000000000002-200-22-222-20000-222-2000000000000000000
χ55444-4-4-444-40000000000000000000-22002-22-2-220000-222-2000000000000000000
χ56444-4-4-444-40000000000000000000-22002-2-222-200002-2-22000000000000000000
χ5744-4-44-44-44400-4-44000000000002-2002-2000000-22-220000000000000000000000
χ5844-4-44-44-44400-4-4400000000000-2200-220000002-22-20000000000000000000000
χ5944-4-4-44-444400-44-4000000000002-200-22000000-222-20000000000000000000000
χ6044-4-4-44-444400-44-400000000000-22002-20000002-2-220000000000000000000000
χ6188-888-8-88-80000000000000000000000000000000000000000000000000000000
χ6288-88-888-8-80000000000000000000000000000000000000000000000000000000
χ6316-16000000008-80000000000000000000000000000000000000000000000000000
χ6416-1600000000-880000000000000000000000000000000000000000000000000000

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