Finite Group Databasebeta

← Group #196437

Character table — Group #196437

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888888888888888888844444444244444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-11111-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111
χ911111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-11-111-1-1
χ1011111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111-11-1-111
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1111-1111-1-1
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-1-11-1-1-111
χ1311111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-11-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1-11-1111-1-1
χ1511111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11-11-1-111
χ1611111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-11-111-1-1
χ1711111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-11-11-1-1i−ii−i
χ1811111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-11-11-111−ii−ii
χ1911111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-11-11-111i−ii−i
χ2011111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-11-11-1-1−ii−ii
χ2111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-11-111-1-1−ii−ii
χ2211111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-11-11-1-111i−ii−i
χ2311111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-11-11-1-111−ii−ii
χ2411111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-11-111-1-1i−ii−i
χ2511111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-11-1-11i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111-111-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111-111-1i−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-11-1-11−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-111-1-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11-1-1111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11-1-1111-1−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-111-1-1-11i−i−ii
χ33222222222222-2-222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ34222222222222-2-222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-222-2-2-2-2222222-2-222-2-222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-2222222-2-222-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ41222-2-2-22-222-2-2002i2i−2i−2i2i2i−2i−2i00000000002i−2i002i−2i002-2002-2i2i2−i2−i2i2i2−i2−i222−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ42222-2-2-22-222-2-2002i2i−2i−2i2i2i−2i−2i00000000002i−2i002i−2i002-2002-2−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000
χ43222-2-2-22-222-2-2002i2i−2i−2i2i2i−2i−2i0000000000−2i2i00−2i2i00-2200-22i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000
χ44222-2-2-22-222-2-2002i2i−2i−2i2i2i−2i−2i0000000000−2i2i00−2i2i00-2200-22−i2−i2i2i2−i2−i2i2i2−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ45222-2-2-22-222-2-200−2i−2i2i2i−2i−2i2i2i00000000002i−2i002i−2i00-2200-22i2i2−i2−i2i2i2−i2−i2−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ46222-2-2-22-222-2-200−2i−2i2i2i−2i−2i2i2i00000000002i−2i002i−2i00-2200-22−i2−i2i2i2−i2−i2i2i222−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000
χ47222-2-2-22-222-2-200−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00−2i2i002-2002-2i2i2−i2−i2i2i2−i2−i2−2−222−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000
χ48222-2-2-22-222-2-200−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00−2i2i002-2002-2−i2−i2i2i2−i2−i2i2i222−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ49222-2-2-22-2-2-222002i2i−2i−2i−2i−2i2i2i00000000002i−2i00−2i2i002-200-2222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000
χ50222-2-2-22-2-2-222002i2i−2i−2i−2i−2i2i2i00000000002i−2i00−2i2i002-200-22−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000
χ51222-2-2-22-2-2-222002i2i−2i−2i−2i−2i2i2i0000000000−2i2i002i−2i00-22002-222−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000
χ52222-2-2-22-2-2-222002i2i−2i−2i−2i−2i2i2i0000000000−2i2i002i−2i00-22002-2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000
χ53222-2-2-22-2-2-22200−2i−2i2i2i2i2i−2i−2i00000000002i−2i00−2i2i00-22002-222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000
χ54222-2-2-22-2-2-22200−2i−2i2i2i2i2i−2i−2i00000000002i−2i00−2i2i00-22002-2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000
χ55222-2-2-22-2-2-22200−2i−2i2i2i2i2i−2i−2i0000000000−2i2i002i−2i002-200-2222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000
χ56222-2-2-22-2-2-22200−2i−2i2i2i2i2i−2i−2i0000000000−2i2i002i−2i002-200-22−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000
χ572-2-222-22-22-22-2002i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000000000
χ582-2-222-22-22-22-2002i−2i2i−2i2i−2i2i−2i000000002-2002-2002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000000000
χ592-2-222-22-22-22-2002i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000000000
χ602-2-222-22-22-22-2002i−2i2i−2i2i−2i2i−2i00000000-2200-2200−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000000000
χ612-2-222-22-22-22-200−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000000000
χ622-2-222-22-22-22-200−2i2i−2i2i−2i2i−2i2i000000002-2002-200−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000000000
χ632-2-222-22-22-22-200−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000000000
χ642-2-222-22-22-22-200−2i2i−2i2i−2i2i−2i2i00000000-2200-22002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000000000
χ652-2-222-22-2-22-22002i−2i2i−2i−2i2i−2i2i000000002-200-22002i−2i00−2i2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000000000
χ662-2-222-22-2-22-22002i−2i2i−2i−2i2i−2i2i000000002-200-22002i−2i00−2i2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ672-2-222-22-2-22-22002i−2i2i−2i−2i2i−2i2i00000000-22002-200−2i2i002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i2−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ682-2-222-22-2-22-22002i−2i2i−2i−2i2i−2i2i00000000-22002-200−2i2i002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i22−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000000000
χ692-2-222-22-2-22-2200−2i2i−2i2i2i−2i2i−2i000000002-200-2200−2i2i002i−2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000000000
χ702-2-222-22-2-22-2200−2i2i−2i2i2i−2i2i−2i000000002-200-2200−2i2i002i−2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ712-2-222-22-2-22-2200−2i2i−2i2i2i−2i2i−2i00000000-22002-2002i−2i00−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i2−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ722-2-222-22-2-22-2200−2i2i−2i2i2i−2i2i−2i00000000-22002-2002i−2i00−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i22−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000000000
χ732-2-2-2-22222-2-22222-2-222-2-22-2-22-22-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ742-2-2-2-22222-2-22222-2-222-2-22-2-22-22-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ752-2-2-2-22222-2-2222-222-2-222-2-2-22-2-22-22000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ762-2-2-2-22222-2-2222-222-2-222-2-2-22-2-22-2200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ772-2-2-2-22222-2-22-2-22-2-222-2-2222-22-22-2200000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ782-2-2-2-22222-2-22-2-22-2-222-2-2222-22-22-220000000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ792-2-2-2-22222-2-22-2-2-222-2-222-222-222-22-200000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000000000
χ802-2-2-2-22222-2-22-2-2-222-2-222-222-222-22-20000000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000000000
χ812-2-2-2-2222-222-2222-2-22-222-2-2-2-22-222-200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ822-2-2-2-2222-222-2222-2-22-222-2-2-2-22-222-20000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ832-2-2-2-2222-222-222-222-22-2-22-2-2-222-2-2200000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ842-2-2-2-2222-222-222-222-22-2-22-2-2-222-2-220000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ852-2-2-2-2222-222-2-2-22-2-22-222-2222-22-2-22000000000000000000000000000000002-2-22-222-2-222-22-2-2200000000000000000000
χ862-2-2-2-2222-222-2-2-22-2-22-222-2222-22-2-2200000000000000000000000000000000-222-22-2-222-2-22-222-200000000000000000000
χ872-2-2-2-2222-222-2-2-2-222-22-2-22222-2-222-2000000000000000000000000000000002-2-22-222-22-2-22-222-200000000000000000000
χ882-2-2-2-2222-222-2-2-2-222-22-2-22222-2-222-200000000000000000000000000000000-222-22-2-22-222-22-2-2200000000000000000000
χ8944-44-4-4-4400004i−4i000000004i−4i00000000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000
χ9044-44-4-4-4400004i−4i000000004i−4i0000000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000
χ9144-44-4-4-440000−4i4i00000000−4i4i00000000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000
χ9244-44-4-4-440000−4i4i00000000−4i4i0000000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000
χ934-44-44-4-4400004i−4i00000000−4i4i0000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ944-44-44-4-4400004i−4i00000000−4i4i000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ954-44-44-4-440000−4i4i000000004i−4i0000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ964-44-44-4-440000−4i4i000000004i−4i000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ9788-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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