Finite Group Databasebeta

← Group #72238437

Character table — Group #72238437

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222244888881616161616161616161616161616161616163232323232323232323232323264646464
order1222222222222222222244444444444444424444444444448888
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111-1-1-1-111-1-11-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-11-1-11111-1-1-1-1-1-111-1-1-1111111-1-1-1-111-1-1
χ6111111111111111111-1-11-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-11-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1
χ91111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1111-1ii−i−iii−i−ii−ii−i
χ101111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1111-1−i−iii−i−iii−ii−ii
χ111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-11-11ii−i−iii−i−i−ii−ii
χ121111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-11-11−i−iii−i−iiii−ii−i
χ131111111111111-1-1-1-11-1-111111-1-111-1-111-1-11-1-11-1ii−i−i−i−iiii−i−ii
χ141111111111111-1-1-1-11-1-111111-1-111-1-111-1-11-1-11-1−i−iiiii−i−i−iii−i
χ151111111111111-1-1-1-11-1-1111-1-1111111-1-1-1-1-11-1-11ii−i−i−i−iii−iii−i
χ161111111111111-1-1-1-11-1-1111-1-1111111-1-1-1-1-11-1-11−i−iiiii−i−ii−i−ii
χ1722222222222222222-222-2220000-2-20000-2-200-200000000000000
χ1822222222222222222-2-2-2-2-2-20000220000-2-200200000000000000
χ192222222222222-2-2-2-2-222-2-2-200002200002200-200000000000000
χ202222222222222-2-2-2-2-2-2-2-2220000-2-200002200200000000000000
χ212222222222-2-2-22-22-2200-2002222000000-22000-2-2000000000000
χ222222222222-2-2-22-22-2200-200-2-2-2-2000000-2200022000000000000
χ232222222222-2-2-22-22-2-20020000000022222-2-2-2000000000000000
χ242222222222-2-2-22-22-2-200200000000-2-2-2-22-222000000000000000
χ252222222222-2-2-2-22-22200-20022-2-20000002-2000-22000000000000
χ262222222222-2-2-2-22-22200-200-2-2220000002-20002-2000000000000
χ272222222222-2-2-2-22-22-20020000000022-2-2-222-2000000000000000
χ282222222222-2-2-2-22-22-200200000000-2-222-22-22000000000000000
χ2944444-4-44-4-4000040-40000000000000000000000000002i−2i2i−2i0000
χ3044444-4-44-4-4000040-4000000000000000000000000000−2i2i−2i2i0000
χ3144444-4-44-4-40000-4040000000000000000000000000002-2-220000
χ3244444-4-44-4-40000-404000000000000000000000000000-222-20000
χ334444-444-4-4-400040-40000000000000000000000002i−2i2i−2i00000000
χ344444-444-4-4-400040-4000000000000000000000000−2i2i−2i2i00000000
χ354444-444-4-4-4000-4040000000000000000000000002-2-2200000000
χ364444-444-4-4-4000-404000000000000000000000000-222-200000000
χ374444-4-4-4-44444-4000000004-400000000000000000000000000000
χ384444-4-4-4-44444-400000000-4400000000000000000000000000000
χ394444-4-4-4-444-4-44000000000000004-400000000000000000000000
χ404444-4-4-4-444-4-4400000000000000-4400000000000000000000000
χ4188-8-8800-80000000000000004i−4i000000000000000000000000000
χ4288-8-8800-8000000000000000−4i4i000000000000000000000000000
χ4388-8-8-8008000000000000000000000004-40000000000000000000
χ4488-8-8-800800000000000000000000000-440000000000000000000
χ458-88-800008-8000000004-400000000000000000000000000000000
χ468-88-800008-800000000-4400000000000000000000000000000000
χ478-88-80000-888-80000000000000000000000000000000000000000
χ488-88-80000-88-880000000000000000000000000000000000000000
χ498-8-8808-800000000000000000000004-4000000000000000000000
χ508-8-8808-80000000000000000000000-44000000000000000000000
χ518-8-880-880000000000000000004-40000000000000000000000000
χ528-8-880-88000000000000000000-440000000000000000000000000

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