Finite Group Databasebeta

← Group #228296

Character table — Group #228296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222444444444444444488888888224488888888888888888888888888888888224444444444448888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1
χ1711111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i111-111-1-1-1-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i1-1i−i
χ1811111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii111-1-1-111-1-111-1-1i−i−i−iiiii−i−i-1-111−i−iii-11−ii
χ1911111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-11-1-1-11111-1-111i−i−i−iii−i−iii11-1-1ii−i−i-11−ii
χ2011111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-11-111-1-111-1-111i−iii−i−i−i−iii-1-111−i−iii1-1i−i
χ2111111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111ii−i−i−i−iiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1111-1-1-1-1-1-111−iiii−i−i−i−iii-1-111−i−iii-11−ii
χ2211111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-11-1-111-1-1-1-111−ii−i−iii−i−iii11-1-1ii−i−i1-1i−i
χ2311111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-11-1-1111111-1-1−ii−i−iiiii−i−i-1-111−i−iii1-1i−i
χ2411111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111ii−i−i−i−iii−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1111-1-11111-1-1−iiii−i−iii−i−i11-1-1ii−i−i-11−ii
χ2511111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-11-1-1-11111-1-111−iiii−i−iii−i−i11-1-1−i−iii-11i−i
χ2611111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-11-111-1-111-1-111−ii−i−iiiii−i−i-1-111ii−i−i1-1−ii
χ2711111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii111-111-1-1-1-111-1-1−ii−i−iii−i−iii11-1-1−i−iii1-1−ii
χ2811111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i111-1-1-111-1-111-1-1−iiii−i−i−i−iii-1-111ii−i−i-11i−i
χ2911111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-11-1-1111111-1-1i−iii−i−i−i−iii-1-111ii−i−i1-1−ii
χ3011111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111−i−iiiii−i−iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1111-1-11111-1-1i−i−i−iii−i−iii11-1-1−i−iii-11i−i
χ3111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111−i−iiiii−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1111-1-1-1-1-1-111i−i−i−iiiii−i−i-1-111ii−i−i-11i−i
χ3211111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-11-1-111-1-1-1-111i−iii−i−iii−i−i11-1-1−i−iii1-1−ii
χ332222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2222200000000000000000000000000-2-20000000000-2-200000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000002200000000002200000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000-2-200000000002200000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000220000000000-2-200000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000-220000000000−2i2i00000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000002-200000000002i−2i00000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000-2200000000002i−2i00000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000002-20000000000−2i2i00000000000000000000
χ41222-2-22-2-222-2-222-2-2-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-200002i−2i2i−2i0000000000000000000000000000
χ42222-2-22-2-222-2-222-2-2-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i00000000-2-222-2-2220000−2i2i−2i2i0000000000000000000000000000
χ43222-2-22-2-222-2-222-2-2-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-20000−2i2i−2i2i0000000000000000000000000000
χ44222-2-22-2-222-2-222-2-2-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-222-2-22200002i−2i2i−2i0000000000000000000000000000
χ45222-2-22-2-2-2-222-2-2222222-2-2-2-20000000000000000000022-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i0000000000000000000000000000
χ46222-2-22-2-2-2-222-2-2222222-2-2-2-20000000000000000000022-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i0000000000000000000000000000
χ47222-2-22-2-2-2-222-2-2222222-2-2-2-200000000000000000000-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i0000000000000000000000000000
χ48222-2-22-2-2-2-222-2-2222222-2-2-2-200000000000000000000-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i0000000000000000000000000000
χ4922-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32-22i−2i00002ζ−2ζ2ζ3−2ζ300000000i2i2−i2−i222−2−21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000i2−i22−21−i−1+i1+i−1−i0000
χ5022-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32-22i−2i00002ζ−2ζ2ζ3−2ζ300000000−i2−i2i2i2−2−222−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000−i2i2−22−1+i1−i−1−i1+i0000
χ5122-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-22−2i2i0000−2ζ2ζ−2ζ32ζ300000000i2i2−i2−i222−2−21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000−i2i2−22−1+i1−i−1−i1+i0000
χ5222-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-22−2i2i0000−2ζ2ζ−2ζ32ζ300000000−i2−i2i2i2−2−222−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000i2−i22−21−i−1+i1+i−1−i0000
χ5322-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32-22i−2i0000−2ζ2ζ−2ζ32ζ300000000i2i2−i2−i222−2−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000i2−i22−2−1+i1−i−1−i1+i0000
χ5422-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32-22i−2i0000−2ζ2ζ−2ζ32ζ300000000−i2−i2i2i2−2−2221−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000−i2i2−221−i−1+i1+i−1−i0000
χ5522-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-22−2i2i00002ζ−2ζ2ζ3−2ζ300000000i2i2−i2−i222−2−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000−i2i2−221−i−1+i1+i−1−i0000
χ5622-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-22−2i2i00002ζ−2ζ2ζ3−2ζ300000000−i2−i2i2i2−2−2221−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000i2−i22−2−1+i1−i−1−i1+i0000
χ5722-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2-2−2i2i00002ζ3−2ζ32ζ−2ζ00000000i2i2−i2−i2−2−2221+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000i2−i2−221+i−1−i1−i−1+i0000
χ5822-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2-2−2i2i00002ζ3−2ζ32ζ−2ζ00000000−i2−i2i2i222−2−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000−i2i22−2−1−i1+i−1+i1−i0000
χ5922-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-222i−2i0000−2ζ32ζ3−2ζ2ζ00000000i2i2−i2−i2−2−2221+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000−i2i22−2−1−i1+i−1+i1−i0000
χ6022-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-222i−2i0000−2ζ32ζ3−2ζ2ζ00000000−i2−i2i2i222−2−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000i2−i2−221+i−1−i1−i−1+i0000
χ6122-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2-2−2i2i0000−2ζ32ζ3−2ζ2ζ00000000i2i2−i2−i2−2−222−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000i2−i2−22−1−i1+i−1+i1−i0000
χ6222-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2-2−2i2i0000−2ζ32ζ3−2ζ2ζ00000000−i2−i2i2i222−2−21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000−i2i22−21+i−1−i1−i−1+i0000
χ6322-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-222i−2i00002ζ3−2ζ32ζ−2ζ00000000i2i2−i2−i2−2−222−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000−i2i22−21+i−1−i1−i−1+i0000
χ6422-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-222i−2i00002ζ3−2ζ32ζ−2ζ00000000−i2−i2i2i222−2−21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000i2−i2−22−1−i1+i−1+i1−i0000
χ652-222-2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2i−2i2i−2i2-22-20000000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ662-222-2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2i2i−2i2i-22-22000000000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ672-222-2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i00000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2i−2i2i−2i2-22-2000000000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ682-222-2-2-222i−2i2i−2i−2i2i−2i2i2i−2i2-22-22i−2i00000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2i2i−2i2i-22-220000000000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ692-222-2-2-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32i−2i2i−2i-22-22000000000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ702-222-2-2-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2i2i−2i2i2-22-20000000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ712-222-2-2-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i00000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32i−2i2i−2i-22-220000000000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000
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χ964-444-4-4-44−4i4i−4i4i4i−4i4i−4i4i−4i-44-444i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-44444-4-4-4-400000000000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ984-4-4444-4-44444-4-4-4-4000000000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ994-4-4444-4-4-4-4-4-4444400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ1004-4-4444-4-4-4-4-4-44444000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ1014-4-4-4-444444-4-4-4-444000000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-444444-4-4-4-44400000000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4444-4-44444-4-4000000004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4444-4-44444-4-400000000−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.