Finite Group Databasebeta

← Group #72319747

Character table — Group #72319747

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222222444444888888888881616161616161616161616161616161616161616323232323232323232323232323232323232
order1222222224444442222222244422444444444444448888444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111
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
χ9111-1-11-1-11-1-1-1-1111111-1-1-1-111-11-11-1iiii−i−i−i−i11-1-111-1-11-1ii−i−iii−i−i1-11-1ii−i−i
χ10111-1-11-1-11-1-1-1-1111111-1-1-1-111-11-11-1iiii−i−i−i−i-1-111-1-111-11ii−i−i−i−iii-111-1−i−iii
χ11111-1-11-1-11-1-1-1-1111111-1-1-1-111-11-11-1−i−i−i−iiiii11-1-111-1-11-1−i−iii−i−iii1-11-1−i−iii
χ12111-1-11-1-11-1-1-1-1111111-1-1-1-111-11-11-1−i−i−i−iiiii-1-111-1-111-11−i−iiiii−i−i-111-1ii−i−i
χ13111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-11-11iiii−i−i−i−i11-1-1-1-111-11−i−iiiii−i−i1-1-11−i−iii
χ14111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-11-11iiii−i−i−i−i-1-11111-1-11-1−i−iii−i−iii-11-11ii−i−i
χ15111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-11-11−i−i−i−iiiii11-1-1-1-111-11ii−i−i−i−iii1-1-11ii−i−i
χ16111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-11-11−i−i−i−iiiii-1-11111-1-11-1ii−i−iii−i−i-11-11−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
χ1922222222222-2-22222-2-22-22-2-2-2-2000000000000222200000000000000-2-2000000
χ2022222222222-2-22222-2-22-22-2-2-2-2000000000000-2-2-2-20000000000000022000000
χ2122222222222-2-222-2-222-22-22-2-2-222220000000000000000000000000000-2-20000
χ2222222222222-2-222-2-222-22-22-2-2-2-2-2-2-20000000000000000000000000000220000
χ23222-2-22-2-22-2-2222222-2-2-22-22-2-2200000000000022-2-200000000000000-22000000
χ24222-2-22-2-22-2-2222222-2-2-22-22-2-22000000000000-2-222000000000000002-2000000
χ25222-2-22-2-22-2-22222-2-2222-22-2-2-222-22-20000000000000000000000000000-220000
χ26222-2-22-2-22-2-22222-2-2222-22-2-2-22-22-2200000000000000000000000000002-20000
χ27222-2-22-2-22-2-2-2-222-2-2-2-2222222-2000000000000000022-2-2-220000000000000000
χ28222-2-22-2-22-2-2-2-222-2-2-2-2222222-20000000000000000-2-2222-20000000000000000
χ2922-222-2-2-222-222-222-22-22-2-222-2-200000000000000000000000000000000002i−2i2i−2i
χ3022-222-2-2-222-222-222-22-22-2-222-2-20000000000000000000000000000000000−2i2i−2i2i
χ3122-222-2-2-222-222-22-22-22-222-22-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ3222-222-2-2-222-222-22-22-22-222-22-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ3322-222-2-2-222-2-2-2-222-2-2222-2-2-22200000000000000000000002i−2i2i−2i000000000000
χ3422-222-2-2-222-2-2-2-222-2-2222-2-2-2220000000000000000000000−2i2i−2i2i000000000000
χ3522-222-2-2-222-2-2-2-22-222-2-2-222-222000000000000000000000000002-22-200000000
χ3622-222-2-2-222-2-2-2-22-222-2-2-222-22200000000000000000000000000-22-2200000000
χ3722-2-2-2-2222-2222-222-2-22-2-222-22-200000000000000000000002-2-22000000000000
χ3822-2-2-2-2222-2222-222-2-22-2-222-22-20000000000000000000000-222-2000000000000
χ3922-2-2-2-2222-2222-22-222-222-2-2-22-2000000000000000000000000002i−2i−2i2i00000000
χ4022-2-2-2-2222-2222-22-222-222-2-2-22-200000000000000000000000000−2i2i2i−2i00000000
χ4122-2-2-2-2222-22-2-2-222-22-2-222-22-2200000000000000000000000000000000002-2-22
χ4222-2-2-2-2222-22-2-2-222-22-2-222-22-220000000000000000000000000000000000-222-2
χ4322-2-2-2-2222-22-2-2-22-22-222-2-222-22000022-2-2-2-22200000000000000000000000000
χ4422-2-2-2-2222-22-2-2-22-22-222-2-222-220000-2-22222-2-200000000000000000000000000
χ45444444444-4-400-4-40000000000000002-22-22-22-200000000000000000000000000
χ46444444444-4-400-4-4000000000000000-22-22-22-2200000000000000000000000000
χ474444-4-44-4-40000000000000000022-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ484444-4-44-4-40000000000000000022-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ494444-4-44-4-400000000000000000-2-222000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ504444-4-44-4-400000000000000000-2-22200000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ51444-44-4-44-4000000000000000002-2-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ52444-44-4-44-4000000000000000002-2-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ53444-44-4-44-400000000000000000-222-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ54444-44-4-44-400000000000000000-222-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ55444-4-44-4-444400-4-40000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ56444-4-44-4-444400-4-4000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5744-444-4-4-44-44004-40000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5844-444-4-4-44-44004-4000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5944-4-4-4-44444-4004-40000000000000002-2-22-222-200000000000000000000000000
χ6044-4-4-4-44444-4004-4000000000000000-222-22-2-2200000000000000000000000000
χ6188-88-88-88-80000000000000000000000000000000000000000000000000000000
χ6288-8-8888-8-80000000000000000000000000000000000000000000000000000000
χ6316-160000000008-8000000000000000000000000000000000000000000000000000
χ6416-16000000000-88000000000000000000000000000000000000000000000000000

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