Finite Group Databasebeta

← Group #386804

Character table — Group #386804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444422222222444444448888888888888888444444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ9111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-111
χ1711111-1-111-1-1-1-11-1-11-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ1811111-1-111-1-1-1-11-1-11-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ1911111-1-111-1-1-1-11-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii
χ2011111-1-111-1-1-1-11-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i
χ2111111-1-111-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11ii−i−iii−i−iii−i−i−i−iii11-1-1-1-111−ii−iii−i−ii
χ2211111-1-111-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11−i−iii−i−iii−i−iiiii−i−i11-1-1-1-111i−ii−i−iii−i
χ2311111-1-111-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11ii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1−ii−ii−iii−i
χ2411111-1-111-1-1-1-11-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1i−ii−ii−i−ii
χ2511111-1-111-1-1-1-11-1-11-1-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1ii−i−i−i−iiiii−i−iii−i−i-1-11111-1-1i−i−ii−ii−ii
χ2611111-1-111-1-1-1-11-1-11-1-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1−i−iiiii−i−i−i−iii−i−iii-1-11111-1-1−iii−ii−ii−i
χ2711111-1-111-1-1-1-11-1-11-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1ii−i−i−i−iii−i−iii−i−iii11-1-1-1-111i−i−iii−ii−i
χ2811111-1-111-1-1-1-11-1-11-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1−i−iiiii−i−iii−i−iii−i−i11-1-1-1-111−iii−i−ii−ii
χ2911111-1-111-1-1-1-11-1-11-1-1-1-1111-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11ii−i−i−i−iiiii−i−i−i−iii-1-111-1-111−iii−i−iii−i
χ3011111-1-111-1-1-1-11-1-11-1-1-1-1111-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111i−i−iii−i−ii
χ3111111-1-111-1-1-1-11-1-11-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11ii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1−iii−ii−i−ii
χ3211111-1-111-1-1-1-11-1-11-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1i−i−ii−iii−i
χ332222222222222222-2-2-2-2-2-2-2-22222222222-2-222-2-20000000000000000-2-2-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000-2-22200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222000000000000000022-2-200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-20000000000000000222200000000000000000000000000000000
χ3722222-2-222-2-2-2-22-2-2-22222-2-2-222-2-222-2-222-2-2-2-2220000000000000000-22-2200000000000000000000000000000000
χ3822222-2-222-2-2-2-22-2-2-22222-2-2-222-2-2-2-222-2-22222-2-20000000000000000-222-200000000000000000000000000000000
χ3922222-2-222-2-2-2-22-2-2-22222-2-2-2-2-22222-2-2-2-22222-2-200000000000000002-2-2200000000000000000000000000000000
χ4022222-2-222-2-2-2-22-2-2-22222-2-2-2-2-222-2-22222-2-2-2-22200000000000000002-22-200000000000000000000000000000000
χ41222-2-222-2-222-2-22-2-2-222-2-22-2200000000000000000000000022-2-222-2-2000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ42222-2-222-2-222-2-22-2-2-222-2-22-2200000000000000000000000022-2-222-2-200000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ43222-2-222-2-222-2-22-2-2-222-2-22-22000000000000000000000000-2-222-2-222000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ44222-2-222-2-222-2-22-2-2-222-2-22-22000000000000000000000000-2-222-2-22200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ45222-2-2-2-2-2-2-2-222222-2-2-2222-2200000000000000000000000022-2-2-2-222000000002-2-2200002-2-220000000000000000
χ46222-2-2-2-2-2-2-2-222222-2-2-2222-2200000000000000000000000022-2-2-2-22200000000-222-20000-222-20000000000000000
χ47222-2-2-2-2-2-2-2-222222-2-2-2222-22000000000000000000000000-2-22222-2-2000000002-2-220000-222-20000000000000000
χ48222-2-2-2-2-2-2-2-222222-2-2-2222-22000000000000000000000000-2-22222-2-200000000-222-200002-2-220000000000000000
χ4922-22-22-22-22-22-2-22-2000000002-22-22-22-22-2002-200i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5022-22-22-22-22-22-2-22-2000000002-22-22-22-22-2002-200−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ5122-22-22-22-22-22-2-22-2000000002-22-2-22-22-2200-2200i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ5222-22-22-22-22-22-2-22-2000000002-22-2-22-22-2200-2200−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5322-22-22-22-22-22-2-22-200000000-22-222-22-2-2200-2200i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5422-22-22-22-22-22-2-22-200000000-22-222-22-2-2200-2200−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ5522-22-22-22-22-22-2-22-200000000-22-22-22-222-2002-200i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ5622-22-22-22-22-22-2-22-200000000-22-22-22-222-2002-200−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5722-22-2-222-2-22-22-2-22000000002-2-222-2-222-200-2200i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ5822-22-2-222-2-22-22-2-22000000002-2-222-2-222-200-2200−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ5922-22-2-222-2-22-22-2-22000000002-2-22-222-2-22002-200i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ6022-22-2-222-2-22-22-2-22000000002-2-22-222-2-22002-200−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ6122-22-2-222-2-22-22-2-2200000000-222-22-2-22-22002-200i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ6222-22-2-222-2-22-22-2-2200000000-222-22-2-22-22002-200−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ6322-22-2-222-2-22-22-2-2200000000-222-2-222-22-200-2200i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ6422-22-2-222-2-22-22-2-2200000000-222-2-222-22-200-2200−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ652-2-22222-2-2-2-2222-2-2-22-22-2-22200000000000000002-22-22-22-20000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ662-2-22222-2-2-2-2222-2-2-22-22-2-22200000000000000002-22-22-22-2000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ672-2-22222-2-2-2-2222-2-2-22-22-2-2220000000000000000-22-22-22-220000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ682-2-22222-2-2-2-2222-2-2-22-22-2-2220000000000000000-22-22-22-22000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ692-2-222-2-2-2-222-2-2222-2-22-22-22200000000000000002-22-2-22-220000000000002-2-2200002-2-2200000000000000000000
χ702-2-222-2-2-2-222-2-2222-2-22-22-22200000000000000002-22-2-22-22000000000000-222-20000-222-200000000000000000000
χ712-2-222-2-2-2-222-2-2222-2-22-22-2220000000000000000-22-222-22-20000000000002-2-220000-222-200000000000000000000
χ722-2-222-2-2-2-222-2-2222-2-22-22-2220000000000000000-22-222-22-2000000000000-222-200002-2-2200000000000000000000
χ73444-4-444-4-444-4-44-4-44-4-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-4-4-4-4-444444444-4-4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-444-4-44-4-44000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ7644-4-444-4-444-4-44-4-4400000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ7744-4-44-44-44-444-4-44-4000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ7844-4-44-44-44-444-4-44-400000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ794-444-44-4-44-444-4-4-440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ804-444-44-4-44-444-4-4-44000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ814-444-4-44-444-4-44-44-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ824-444-4-44-444-4-44-44-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ834-44-444-44-4-44-44-44-40000000000000000004i−4i004i−4i0000000000000000000000000000000000000000000000000000
χ844-44-444-44-4-44-44-44-4000000000000000000−4i4i00−4i4i0000000000000000000000000000000000000000000000000000
χ854-44-44-444-44-44-4-4-440000000000000000004i−4i00−4i4i0000000000000000000000000000000000000000000000000000
χ864-44-44-444-44-44-4-4-44000000000000000000−4i4i004i−4i0000000000000000000000000000000000000000000000000000
χ874-4-44444-4-4-4-4444-4-44-44-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-4-4-4-444-4-444444-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44444-4-4-4-444444-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4-4-44444-4-4-4-4444-4-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4-4-44444444-4-44-444-4-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4-4-44444444-4-4-44-4-4444-400000000000000000000000000000000000000000000000000000000000000000000

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