Finite Group Databasebeta

← Group #226813

Character table — Group #226813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444444444888888888888888888888888444444448888888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-11-1111-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111111111-1-1-1-11111-11-11-1-1-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-111111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111111111-1-1-1-11-11-1-1-1-1-1
χ1711111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111i−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-1-1-111i−ii−iii−i−i−i−iii−i−iii−i−iii1-1-11i−i−ii
χ2011111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-11111-1-1i−ii−i−i−iiiii−i−i−i−iii−i−iii-111-1−iii−i
χ2111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-1−ii−ii
χ2211111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111-1-111−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111i−ii−i
χ2311111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-1-1-111−ii−ii−i−iiiii−i−iii−i−iii−i−i1-1-11−iii−i
χ2411111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-11111-1-1−ii−iiii−i−i−i−iiiii−i−iii−i−i-111-1i−i−ii
χ2511111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-1111111-1-111-1-1i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-111−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-1-111-1-111i−i−ii−i−iiiii−i−iii−i−i−i−iii11-1-1i−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-111-1-1-1-111i−i−iiii−i−iii−i−i−i−iiiii−i−i-111-1−ii−ii
χ2811111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1-1-11111-1-1i−i−ii−i−iii−i−iii−i−iiiii−i−i1-1-11i−ii−i
χ2911111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-1111111-1-111-1-1−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-111i−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-1-111-1-111−iii−iii−i−i−i−iii−i−iiiii−i−i11-1-1−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-111-1-1-1-111−iii−i−i−iii−i−iiiii−i−i−i−iii-111-1i−ii−i
χ3211111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-1-11111-1-1−iii−iii−i−iii−i−iii−i−i−i−iii1-1-11−ii−ii
χ332222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222222222000000000000000000000000-2-2-2-2000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-222000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000022-2-2000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000−2i2i−2i2i000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000002i−2i2i−2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i000000000000000000000000
χ41222-2-22-2-22222-2-2-2-2-2-222-2-222000000000000000022-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ42222-2-22-2-22222-2-2-2-2-2-222-2-222000000000000000022-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ43222-2-22-2-22222-2-2-2-2-2-222-2-2220000000000000000-2-222-2-222000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ44222-2-22-2-22222-2-2-2-2-2-222-2-2220000000000000000-2-222-2-22200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ45222-2-22-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ46222-2-22-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ47222-2-22-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ48222-2-22-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ4922-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32−22−2i2−i2i2−i222−2−2i2i2−i2−i2000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ5022-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i00002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3−22−22−i2i2−i2i2−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ5122-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ32−22−2i2−i2i2−i222−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ5222-22-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i0000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−22−22−i2i2−i2i2−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ5322-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32−22−2i2−i2i2−i2−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ5422-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i00002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−22−22−i2i2−i2i222−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ5522-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i0000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32−22−2i2−i2i2−i2−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ5622-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i0000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−22−22−i2i2−i2i222−2−2i2i2−i2−i2000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ5722-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i00002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ2−22−2−i2i2−i2i222−2−2−i2−i2i2i200000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ5822-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i00002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ−22−22i2−i2i2−i2−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ5922-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ2−22−2−i2i2−i2i222−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ6022-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ−22−22i2−i2i2−i2−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ6122-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i00002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2−22−2−i2i2−i2i2−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ6222-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i00002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ−22−22i2−i2i2−i222−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ6322-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i0000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ2−22−2−i2i2−i2i2−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ6422-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i0000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−22−22i2−i2i2−i222−2−2−i2−i2i2i200000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ652-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i0000000000000000000000002-22-22i−2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ662-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i0000000000000000000000002-22-22i−2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ672-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i000000000000000000000000-22-22−2i2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ682-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2-22-22i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ692-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i0000000000000000000000002-22-2−2i2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ702-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ712-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i000000000000000000000000-22-222i−2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ722-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i000000000000000000000000-22-222i−2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ73444-4-44-4-44444-4-4-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-44-4-4-4-4-4-44444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-444i4i−4i−4i−4i−4i4i4i00000000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7644-4-44-4-444i4i−4i−4i−4i−4i4i4i000000000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7744-4-44-4-44−4i−4i4i4i4i4i−4i−4i00000000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7844-4-44-4-44−4i−4i4i4i4i4i−4i−4i000000000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000000000000
χ794-444-4-4-444i−4i4i−4i−4i4i−4i4i4i−4i-444-4−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ804-444-4-4-444i−4i4i−4i−4i4i−4i4i−4i4i4-4-444i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ814-444-4-4-44−4i4i−4i4i4i−4i4i−4i4i−4i4-4-44−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ824-444-4-4-44−4i4i−4i4i4i−4i4i−4i−4i4i-444-44i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-44-44-44-44i−4i4i−4i4i−4i4i−4i−4i4i-44-44−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ844-44-44-44-4−4i4i−4i4i−4i4i−4i4i4i−4i-44-444i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-4-44-4-44-444-40000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ864-4-4444-4-44-4-44-444-4000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-4-444-44-4-440000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-4-4-444-44-4-44000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44444-4-444-4-440000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ904-4-4-4-44444-4-444-4-4400000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ914-4-4-4-4444-444-4-444-40000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-444-400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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