Finite Group Databasebeta

← Group #243162

Character table — Group #243162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ292222-2-2-2-22222-2-2-2-222-2-22-22222-2-22-2-2-22-22-2000000000000000000000000000000000000000022-2-222-2-200000000
χ302222-2-2-2-22222-2-2-2-222-2-22-22222-2-22-2-2-22-22-20000000000000000000000000000000000000000-2-222-2-22200000000
χ312222-2-2-2-22222-2-2-2-222-2-22-2-2-2-2-2222-222-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ322222-2-2-2-22222-2-2-2-222-2-22-2-2-2-2-2222-222-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ332222-2-2-2-22222-2-2-2-2-2-222-222222-2-2-22-2-2-22-220000000000000000000000000000000022-2-222-2-20000000000000000
χ342222-2-2-2-22222-2-2-2-2-2-222-222222-2-2-22-2-2-22-2200000000000000000000000000000000-2-222-2-2220000000000000000
χ352222-2-2-2-22222-2-2-2-2-2-222-22-2-2-2-222-22222-22-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ362222-2-2-2-22222-2-2-2-2-2-222-22-2-2-2-222-22222-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ372222-2-2-2-2-2-2-2-2222222-2-2-2222-2-222-22-2-2-222-20000000000000000000000000000000022-2-2-2-2220000000000000000
χ382222-2-2-2-2-2-2-2-2222222-2-2-2222-2-222-22-2-2-222-200000000000000000000000000000000-2-22222-2-20000000000000000
χ392222-2-2-2-2-2-2-2-2222222-2-2-22-2-222-2-2-22222-2-220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ402222-2-2-2-2-2-2-2-2222222-2-2-22-2-222-2-2-22222-2-22000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ412222-2-2-2-2-2-2-2-22222-2-2222-222-2-2222-2-2-22-2-22000000000000000000000000000000000000000022-2-2-2-22200000000
χ422222-2-2-2-2-2-2-2-22222-2-2222-222-2-2222-2-2-22-2-220000000000000000000000000000000000000000-2-22222-2-200000000
χ432222-2-2-2-2-2-2-2-22222-2-2222-2-2-222-2-22-222-222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-2-2-2-2-2-22222-2-2222-2-2-222-2-22-222-222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ4522-2-222-2-222-2-222-2-22-22-22-2000000-22000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−2000000000000000000000000
χ4622-2-222-2-222-2-222-2-22-22-22-2000000-22000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−22000000000000000000000000
χ4722-2-222-2-222-2-222-2-22-22-22-2000000-22000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−22000000000000000000000000
χ4822-2-222-2-222-2-222-2-22-22-22-2000000-22000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−2000000000000000000000000
χ4922-2-222-2-222-2-222-2-2-22-22-220000002-2000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ5022-2-222-2-222-2-222-2-2-22-22-220000002-2000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ5122-2-222-2-222-2-222-2-2-22-22-220000002-2000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ5222-2-222-2-222-2-222-2-2-22-22-220000002-2000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ5322-2-222-2-2-2-222-2-2222-22-2-220000002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i2000000000000000000000000
χ5422-2-222-2-2-2-222-2-2222-22-2-220000002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i2000000000000000000000000
χ5522-2-222-2-2-2-222-2-2222-22-2-220000002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i2000000000000000000000000
χ5622-2-222-2-2-2-222-2-2222-22-2-220000002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i2000000000000000000000000
χ5722-2-222-2-2-2-222-2-222-22-222-2000000-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−22000000000000000000000000
χ5822-2-222-2-2-2-222-2-222-22-222-2000000-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i002i−2i−22−222−22−2000000000000000000000000
χ5922-2-222-2-2-2-222-2-222-22-222-2000000-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−2000000000000000000000000
χ6022-2-222-2-2-2-222-2-222-22-222-2000000-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−22000000000000000000000000
χ612-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22i−2i2i−2i002-2000000002i−2i2i−2i00002-22-20000000000000000i2−i2i2−i22−22−22−22−2i2−i2i2−i200000000
χ622-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22i−2i2i−2i002-2000000002i−2i2i−2i00002-22-20000000000000000−i2i2−i2i2−22−22−22−22−i2i2−i2i200000000
χ632-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22i−2i2i−2i002-200000000−2i2i−2i2i0000-22-220000000000000000i2−i2i2−i22−22−2−22−22−i2i2−i2i200000000
χ642-22-22-22-22i−2i2i−2i2i−2i2i−2i0000002-22i−2i2i−2i002-200000000−2i2i−2i2i0000-22-220000000000000000−i2i2−i2i2−22−222−22−2i2−i2i2−i200000000
χ652-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000002-2−2i2i−2i2i002-2000000002i−2i2i−2i0000-22-220000000000000000i2−i2i2−i2−22−222−22−2−i2i2−i2i200000000
χ662-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000002-2−2i2i−2i2i002-2000000002i−2i2i−2i0000-22-220000000000000000−i2i2−i2i22−22−2−22−22i2−i2i2−i200000000
χ672-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000002-2−2i2i−2i2i002-200000000−2i2i−2i2i00002-22-20000000000000000i2−i2i2−i2−22−22−22−22i2−i2i2−i200000000
χ682-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000002-2−2i2i−2i2i002-200000000−2i2i−2i2i00002-22-20000000000000000−i2i2−i2i22−22−22−22−2−i2i2−i2i200000000
χ692-22-2-22-222i−2i2i−2i−2i2i−2i2i0000002-22i−2i−2i2i00-2200002i−2i2i−2i00002-22-200000000000000000000i2−i2−i2i22−2−222−2−22i2−i2−i2i200000000
χ702-22-2-22-222i−2i2i−2i−2i2i−2i2i0000002-22i−2i−2i2i00-2200002i−2i2i−2i00002-22-200000000000000000000−i2i2i2−i2−222−2−222−2−i2i2i2−i200000000
χ712-22-2-22-222i−2i2i−2i−2i2i−2i2i0000002-22i−2i−2i2i00-220000−2i2i−2i2i0000-22-2200000000000000000000i2−i2−i2i22−2−22−222−2−i2i2i2−i200000000
χ722-22-2-22-222i−2i2i−2i−2i2i−2i2i0000002-22i−2i−2i2i00-220000−2i2i−2i2i0000-22-2200000000000000000000−i2i2i2−i2−222−22−2−22i2−i2−i2i200000000
χ732-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000002-2−2i2i2i−2i00-2200002i−2i2i−2i0000-22-2200000000000000000000i2−i2−i2i2−222−22−2−22−i2i2i2−i200000000
χ742-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000002-2−2i2i2i−2i00-2200002i−2i2i−2i0000-22-2200000000000000000000−i2i2i2−i22−2−22−222−2i2−i2−i2i200000000
χ752-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000002-2−2i2i2i−2i00-220000−2i2i−2i2i00002-22-200000000000000000000i2−i2−i2i2−222−2−222−2i2−i2−i2i200000000
χ762-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000002-2−2i2i2i−2i00-220000−2i2i−2i2i00002-22-200000000000000000000−i2i2i2−i22−2−222−2−22−i2i2i2−i200000000
χ7744-4-4-4-44444-4-4-4-4444-4-4444000000-4-400000000000000000000000000000000000000000000000000000000000000
χ7844-4-4-4-44444-4-4-4-444-444-4-4-40000004400000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-4-444-4-44444-4-44-4-44-4-40000004400000000000000000000000000000000000000000000000000000000000000
χ8044-4-4-4-444-4-44444-4-4-444-444000000-4-400000000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-44i−4i4i−4i4i−4i4i−4i000000-44−4i4i−4i4i00-44000000000000000000000000000000000000000000000000000000000000
χ824-44-44-44-4−4i4i−4i4i−4i4i−4i4i000000-444i−4i4i−4i00-44000000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-444i−4i4i−4i−4i4i−4i4i000000-44−4i4i4i−4i004-4000000000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44−4i4i−4i4i4i−4i4i−4i000000-444i−4i−4i4i004-4000000000000000000000000000000000000000000000000000000000000
χ854-4-444-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000022−22−22220000−2i22i22i2−2i20000000000000000000000000000000000000000
χ864-4-444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000−222222−2200002i2−2i2−2i22i20000000000000000000000000000000000000000
χ874-4-444-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000022−22−222200002i2−2i2−2i22i20000000000000000000000000000000000000000
χ884-4-444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000−222222−220000−2i22i22i2−2i20000000000000000000000000000000000000000
χ894-4-44-444-44i−4i−4i4i−4i4i4i−4i0000000000000000000022−22−22220000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-4-44-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000−222222−2200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-44-444-4−4i4i4i−4i4i−4i−4i4i0000000000000000000022−22−222200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ924-4-44-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000−222222−220000−2i22i22i2−2i200000000000000000000000000000000000000000000

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