Finite Group Databasebeta

← Group #218449

Character table — Group #218449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444448888888888888888888888888888444444888888888888888888888824444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111
χ9111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ13111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ1711111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1i−iii−i−iii−i−iii−i−iii−i−i11-1-11-11-11-1i−i
χ1811111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-1-1-111i−i−i−iii−i−iii−i−iiiii−i−i11-1-1-11-11-11−ii
χ1911111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-111111-111-1-1i−i−i−iiiii−i−i−i−iii−i−iii-1-111-111-1-11i−i
χ2011111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-111111-1-1-111i−iii−i−i−i−iiiii−i−i−i−iii-1-1111-1-111-1−ii
χ2111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-111111-111-1-1−iiii−i−i−i−iiiii−i−iii−i−i-1-111-111-1-11−ii
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-111111-1-1-111−ii−i−iiiii−i−i−i−iiiii−i−i-1-1111-1-111-1i−i
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11-111-1-1−ii−i−iii−i−iii−i−iii−i−iii11-1-11-11-11-1−ii
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11-1-1-111−iiii−i−iii−i−iii−i−i−i−iii11-1-1-11-11-11i−i
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1111-1-1i−iii−i−iii−i−i−i−iii−i−iii11-1-1-11-111-1−ii
χ2611111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-11-1-111i−i−i−iii−i−iiiii−i−i−i−iii11-1-11-11-1-11i−i
χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1-1111-1-1i−i−i−iiiii−i−iii−i−iii−i−i-1-1111-1-11-11−ii
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1-11-1-111i−iii−i−i−i−iii−i−iiiii−i−i-1-111-111-11-1i−i
χ2911111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-1111-1-1−iiii−i−i−i−iii−i−iii−i−iii-1-1111-1-11-11i−i
χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-11-1-111−ii−i−iiiii−i−iii−i−i−i−iii-1-111-111-11-1−ii
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1111-1-1−ii−i−iii−i−iiiii−i−iii−i−i11-1-1-11-111-1i−i
χ3211111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−iiii−i−iii−i−i−i−iiiii−i−i11-1-11-11-1-11−ii
χ332222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-222220000000000000000-2-20000-2-20000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-20000220000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000220000-2-20000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000220000220000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000-220000−2i2i0000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000-2200002i−2i0000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000002-20000−2i2i0000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000002-200002i−2i0000000000000000000000000000
χ41222-2-2-22-22i−2i2i2i−2i−2i2i−2i000000002-22i−2i2ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i22−2−2i2i2−i2−i2000000000000000000001+i−1−i1−i−1+i2−2i2−i200000000
χ42222-2-2-22-22i−2i2i2i−2i−2i2i−2i000000002-22i−2i2ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i−22−i2i200000000
χ43222-2-2-22-22i−2i2i2i−2i−2i2i−2i000000002-22i−2i−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i−22−i2i200000000
χ44222-2-2-22-22i−2i2i2i−2i−2i2i−2i000000002-22i−2i−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i22−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i2−2i2−i200000000
χ45222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i2−2i2−i200000000
χ46222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i22−2−2i2i2−i2−i2000000000000000000001+i−1−i1−i−1+i−22−i2i200000000
χ47222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000000-22−2i2i−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i22−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i−22−i2i200000000
χ48222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000000-22−2i2i−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i2−2i2−i200000000
χ49222-2-2-22-2−2i2i−2i−2i2i2i−2i2i000000002-2−2i2i2ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i−22i2−i200000000
χ50222-2-2-22-2−2i2i−2i−2i2i2i−2i2i000000002-2−2i2i2ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i22−2−2−i2−i2i2i200000000000000000000−1+i1−i−1−i1+i2−2−i2i200000000
χ51222-2-2-22-2−2i2i−2i−2i2i2i−2i2i000000002-2−2i2i−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i22−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i2−2−i2i200000000
χ52222-2-2-22-2−2i2i−2i−2i2i2i−2i2i000000002-2−2i2i−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i−22i2−i200000000
χ53222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000000-222i−2i2ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i22−2−2−i2−i2i2i200000000000000000000−1+i1−i−1−i1+i−22i2−i200000000
χ54222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000000-222i−2i2ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i2−2−i2i200000000
χ55222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000000-222i−2i−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i2−2−i2i200000000
χ56222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000000-222i−2i−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i22−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i−22i2−i200000000
χ5722-22-2-2-222i−2i2i−2i2i−2i−2i2i2-22i−2i2-22i−2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000002i−2i2-2002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ5822-22-2-2-222i−2i2i−2i2i−2i−2i2i2-22i−2i2-22i−2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000−2i2i-2200−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ5922-22-2-2-222i−2i2i−2i2i−2i−2i2i2-22i−2i2-22i−2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000002i−2i2-200−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6022-22-2-2-222i−2i2i−2i2i−2i−2i2i2-22i−2i2-22i−2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000−2i2i-22002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6122-22-2-2-22−2i2i−2i2i−2i2i2i−2i2-2−2i2i2-2−2i2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000002i−2i-2200−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ6222-22-2-2-22−2i2i−2i2i−2i2i2i−2i2-2−2i2i2-2−2i2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000−2i2i2-2002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ6322-22-2-2-22−2i2i−2i2i−2i2i2i−2i2-2−2i2i2-2−2i2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000002i−2i-22002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ6422-22-2-2-22−2i2i−2i2i−2i2i2i−2i2-2−2i2i2-2−2i2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000−2i2i2-200−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ652-2-222-22-22i−2i−2i−2i2i2i2i−2i2-2−2i2i-222i−2i0000000000000000000000002-22-22i−2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ662-2-222-22-22i−2i−2i−2i2i2i2i−2i2-2−2i2i-222i−2i0000000000000000000000002-22-22i−2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ672-2-222-22-22i−2i−2i−2i2i2i2i−2i2-2−2i2i-222i−2i000000000000000000000000-22-22−2i2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ682-2-222-22-22i−2i−2i−2i2i2i2i−2i2-2−2i2i-222i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ692-2-222-22-2−2i2i2i2i−2i−2i−2i2i2-22i−2i-22−2i2i0000000000000000000000002-22-2−2i2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ702-2-222-22-2−2i2i2i2i−2i−2i−2i2i2-22i−2i-22−2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ712-2-222-22-2−2i2i2i2i−2i−2i−2i2i2-22i−2i-22−2i2i000000000000000000000000-22-222i−2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ722-2-222-22-2−2i2i2i2i−2i−2i−2i2i2-22i−2i-22−2i2i000000000000000000000000-22-222i−2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ7344-44-4-4-444i−4i4i−4i4i−4i−4i4i-44−4i4i-44−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ7444-44-4-4-44−4i4i−4i4i−4i4i4i−4i-444i−4i-444i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4444-4-44-4-400000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ7644-4-444-4-4444-4-44-4-4000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ7744-4-444-4-4-4-4-444-4440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7844-4-444-4-4-4-4-444-444000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ794-444-44-4-444-444-4-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ804-444-44-4-444-444-4-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ814-444-44-4-4-4-44-4-44444444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ824-444-44-4-4-4-44-4-4444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
χ834-44-44-4-444i−4i−4i4i−4i4i−4i4i00000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000000000000000
χ844-44-44-4-444i−4i−4i4i−4i4i−4i4i0000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000000000000000
χ854-44-44-4-44−4i4i4i−4i4i−4i4i−4i00000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000000000000000
χ864-44-44-4-44−4i4i4i−4i4i−4i4i−4i0000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000000000000000
χ874-4-444-44-44i−4i−4i−4i4i4i4i−4i-444i−4i4-4−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-44-4−4i4i4i4i−4i−4i−4i4i-44−4i4i4-44i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-444444-4-4-4-4440000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ904-4-4-4-444444-4-4-4-44400000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ914-4-4-4-4444-4-44444-4-40000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ924-4-4-4-4444-4-44444-4-400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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