Finite Group Databasebeta

← Group #72319213

Character table — Group #72319213

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111222222222222222244444444444444444444444444444888888888888888888888888888888888161616161616161616161616161616161616161616163232323232323232
order12224444444488888888222444488888888888888161616161616161624444488888888888888816161616161616161616161644448888888888161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-11-1-1111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-1111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111
χ811111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ9111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-11111111111-1111-1-1111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-11111111111-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ11111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-11111-1-1-1-1111111-1-1-1-111
χ12111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ13111111111111-1-1-1-11111-1-111111-1-1-1-1-1-111-1-1-1-111111111111-1-1-1111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ14111111111111-1-1-1-11111-1-111111-1-1-1-1-1-111-1-1-1-111111111111-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111111-1-1-1-11111-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111111111-1-1-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1111111111111-11-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1711111111-1-1-1-11111111111-1111-111-1-1-1-1-1-11111111111-1-1-1-1-11-1-11-1-11111ii−i−iii−i−i-1-111-1-11111-1-1-1-1ii−i−i-1-1i−ii−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ1811111111-1-1-1-11111111111-1111-111-1-1-1-1-1-11111111111-1-1-1-1-11-1-11-1-11111−i−iii−i−iii-1-111-1-11111-1-1-1-1−i−iii-1-1−ii−ii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ1911111111-1-1-1-11111111111-1111-111-1-1-1-1-1-1111111-1-1-1-11111-11-1-11-1-11111ii−i−i−i−iii-1-1-1-111-1-1-1-11111ii−i−i-1-1i−i−ii−i−iii-1-111-1-111i−ii−i−ii−ii
χ2011111111-1-1-1-11111111111-1111-111-1-1-1-1-1-1111111-1-1-1-11111-11-1-11-1-11111−i−iiiii−i−i-1-1-1-111-1-1-1-11111−i−iii-1-1−iii−iii−i−i-1-111-1-111−ii−iii−ii−i
χ2111111111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1-1-11111111111-1-1-1-11-111-11-1-1-1-1-1ii−i−iii−i−i-1-111-1-11111-1-1-1-1ii−i−i11i−ii−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ2211111111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1-1-11111111111-1-1-1-11-111-11-1-1-1-1-1−i−iii−i−iii-1-111-1-11111-1-1-1-1−i−iii11−ii−ii−i−iii-1-111-1-111i−ii−ii−ii−i
χ2311111111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1-1-1111111-1-1-1-111111-111-11-1-1-1-1-1ii−i−i−i−iii-1-1-1-111-1-1-1-11111ii−i−i11i−i−ii−i−iii11-1-111-1-1−ii−iii−ii−i
χ2411111111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1-1-1111111-1-1-1-111111-111-11-1-1-1-1-1−i−iiiii−i−i-1-1-1-111-1-1-1-11111−i−iii11−iii−iii−i−i11-1-111-1-1i−ii−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-11-111-1-1ii−i−iii−i−i1111-1-1-1-1-1-11111−i−iii-11i−ii−i−i−iii11-1-1-1-111i−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-11-111-1-1−i−iii−i−iii1111-1-1-1-1-1-11111ii−i−i-11−ii−iiii−i−i11-1-1-1-111−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-111-1-1ii−i−i−i−iii11-1-1111111-1-1-1-1−i−iii-11i−i−iiii−i−i-1-11111-1-1i−i−ii−iii−i
χ2811111111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-111-1-1−i−iiiii−i−i11-1-1111111-1-1-1-1ii−i−i-11−iii−i−i−iii-1-11111-1-1−iii−ii−i−ii
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111ii−i−iii−i−i1111-1-1-1-1-1-11111−i−iii1-1i−ii−i−i−iii-1-11111-1-1−iii−i−iii−i
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111−i−iii−i−iii1111-1-1-1-1-1-11111ii−i−i1-1−ii−iiii−i−i-1-11111-1-1i−i−iii−i−ii
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111ii−i−i−i−iii11-1-1111111-1-1-1-1−i−iii1-1i−i−iiii−i−i11-1-1-1-111−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111−i−iiiii−i−i11-1-1111111-1-1-1-1ii−i−i1-1−iii−i−i−iii11-1-1-1-111i−i−ii−iii−i
χ332222222222222222-2-2-2-22222222222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2-200000000-2-20000000000000000-2-2000000000000000000000000
χ342222222222222222-2-2-2-2-2-22-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2222200000000-2-2000000000000000022000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2222-2-222-2-2-2-2-2-2-2-22222-2-200000000-2222-2-2-2-2-22200000000220000000000000000-22000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2000000002-2-2-222-222-2-2000000002200000000000000002-2000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2222-222-2-2-2-222-2-2-2-2-2-200000000-22-2-22-22-2-2-2-20000000022000000000000000022000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-22-222-2-2-2-222-2-2-2-2-2-2000000002-222-222222200000000220000000000000000-2-2000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-22-2-2-22222222222-2-20000000022-2-2-222-2-22200000000-2-200000000000000002-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-22222222222-2-200000000-2-2222-2222-2-200000000-2-20000000000000000-22000000000000000000000000
χ41222222-2-222-2-22222000022222-2-2-2-222-2-200000000i2i2−i2−i2i2i2−i2−i22-22-2-2-2000000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ42222222-2-222-2-22222000022222-2-2-2-222-2-200000000−i2−i2i2i2−i2−i2i2i22-22-2-2-2000000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ43222222-2-222-2-222220000-2-22-2-2-2-2-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2-22-2222000000000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ44222222-2-222-2-222220000-2-22-2-2-2-2-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2-22-2222000000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ45222222-2-222-2-2-2-2-2-20000222-2-2-2-222-2-22200000000i2i2−i2−i2i2i2−i2−i2-2-22-222000000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000000000i2−i2i2−i2−i2i2−i2i200000000
χ46222222-2-222-2-2-2-2-2-20000222-2-2-2-222-2-22200000000−i2−i2i2i2−i2−i2i2i2-2-22-222000000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200000000000000−i2i2−i2i2i2−i2i2−i200000000
χ47222222-2-222-2-2-2-2-2-20000-2-2222-2-222-2-22200000000i2i2−i2−i2i2i2−i2−i222-22-2-2000000000000000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200000000000000−i2i2−i2i2i2−i2i2−i200000000
χ48222222-2-222-2-2-2-2-2-20000-2-2222-2-222-2-22200000000−i2−i2i2i2−i2−i2i2i222-22-2-2000000000000000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200000000000000i2−i2i2−i2−i2i2−i2i200000000
χ49222222-2-2-2-2222222000022-222-22-2-2-2-22200000000i2i2−i2−i2−i2−i2i2i2-2-2-22-22000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2i2−i2−i2i200000000
χ50222222-2-2-2-2222222000022-222-22-2-2-2-22200000000−i2−i2i2i2i2i2−i2−i2-2-2-22-22000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2−i2i2i2−i200000000
χ51222222-2-2-2-22222220000-2-2-2-2-2-22-2-2-2-22200000000i2i2−i2−i2−i2−i2i2i2222-22-2000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2−i2i2i2−i200000000
χ52222222-2-2-2-22222220000-2-2-2-2-2-22-2-2-2-22200000000−i2−i2i2i2i2i2−i2−i2222-22-2000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2i2−i2−i2i200000000
χ53222222-2-2-2-222-2-2-2-2000022-2-2-2-222222-2-200000000i2i2−i2−i2−i2−i2i2i22-2-222-2000000000000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2−i2i2i2−i200000000
χ54222222-2-2-2-222-2-2-2-2000022-2-2-2-222222-2-200000000−i2−i2i2i2i2i2−i2−i22-2-222-2000000000000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2i2−i2−i2i200000000
χ55222222-2-2-2-222-2-2-2-20000-2-2-222-222222-2-200000000i2i2−i2−i2−i2−i2i2i2-222-2-22000000000000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2i2−i2−i2i200000000
χ56222222-2-2-2-222-2-2-2-20000-2-2-222-222222-2-200000000−i2−i2i2i2i2i2−i2−i2-222-2-22000000000000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2−i2i2i2−i200000000
χ572222-2-22222220000222200-200-2-2000000220000-2-222222222000000-200002222222200-2-2-2-200000000000000-2-2-2-200000000000000000000
χ582222-2-22222220000222200-200-2-2000000220000-2-222222222000000-20000-2-2-2-2-2-2-2-200-2-2-2-200000000000000222200000000000000000000
χ592222-2-22222220000222200-200-2-2000000220000-2-2-2-2-2-2-2-2-2-2000000-200002222-2-2-2-200222200000000000000-2-22200000000000000000000
χ602222-2-22222220000222200-200-2-2000000220000-2-2-2-2-2-2-2-2-2-2000000-20000-2-2-2-222220022220000000000000022-2-200000000000000000000
χ612222-2-222-2-2-2-20000222200200-22000000-2-20000-2-22222-2-2-2-2000000200002i2i−2i−2i2i2i−2i−2i00-2-22200000000000000−2i2i−2i2i00000000000000000000
χ622222-2-222-2-2-2-20000222200200-22000000-2-20000-2-22222-2-2-2-200000020000−2i−2i2i2i−2i−2i2i2i00-2-222000000000000002i−2i2i−2i00000000000000000000
χ632222-2-222-2-2-2-20000222200200-22000000-2-20000-2-2-2-2-2-22222000000200002i2i−2i−2i−2i−2i2i2i0022-2-200000000000000−2i2i2i−2i00000000000000000000
χ642222-2-222-2-2-2-20000222200200-22000000-2-20000-2-2-2-2-2-2222200000020000−2i−2i2i2i2i2i−2i−2i0022-2-2000000000000002i−2i−2i2i00000000000000000000
χ6522-2-2002-22i−2i2i−2ii2i2−i2−i222-2-20000000i2−i22−22−22i−2ii2i2−i2−i2002-22-22i−2i2i−2i000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32−20000i2−i2i2−i22−22−21−i−1+i1+i−1−i0000001−i−1+i1+i−1−i0000000000000000
χ6622-2-2002-22i−2i2i−2ii2i2−i2−i222-2-20000000i2−i22−22−22i−2ii2i2−i2−i2002-22-22i−2i2i−2i00000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ32−20000i2−i2i2−i22−22−2−1+i1−i−1−i1+i000000−1+i1−i−1−i1+i0000000000000000
χ6722-2-2002-22i−2i2i−2ii2i2−i2−i222-2-20000000i2−i22−22−22i−2ii2i2−i2−i200-22-22−2i2i−2i2i000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32−20000−i2i2−i2i2−22−221−i−1+i1+i−1−i000000−1+i1−i−1−i1+i0000000000000000
χ6822-2-2002-22i−2i2i−2ii2i2−i2−i222-2-20000000i2−i22−22−22i−2ii2i2−i2−i200-22-22−2i2i−2i2i00000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32−20000−i2i2−i2i2−22−22−1+i1−i−1−i1+i0000001−i−1+i1+i−1−i0000000000000000
χ6922-2-2002-22i−2i2i−2i−i2−i2i2i222-2-20000000−i2i2−22−222i−2i−i2−i2i2i2002-22-22i−2i2i−2i000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3−220000−i2i2−i2i2−22−22−1+i1−i−1−i1+i000000−1+i1−i−1−i1+i0000000000000000
χ7022-2-2002-22i−2i2i−2i−i2−i2i2i222-2-20000000−i2i2−22−222i−2i−i2−i2i2i2002-22-22i−2i2i−2i00000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−220000−i2i2−i2i2−22−221−i−1+i1+i−1−i0000001−i−1+i1+i−1−i0000000000000000
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χ7222-2-2002-22i−2i2i−2i−i2−i2i2i222-2-20000000−i2i2−22−222i−2i−i2−i2i2i200-22-22−2i2i−2i2i00000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−220000i2−i2i2−i22−22−21−i−1+i1+i−1−i000000−1+i1−i−1−i1+i0000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.