Finite Group Databasebeta

← Group #226402

Character table — Group #226402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444444444444888888888888888844444444444444444444888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ2011111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiii−ii−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−ii−iii−ii−i
χ2311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−ii−iii−ii−i
χ2411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−ii−ii−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiii−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−ii−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ332222222222222222-2-2-2-222222222-2-2-2-20000000000000000-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-222222222-2-2-2-20000000000000000-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-22222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-222-2-20000000022-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000002-22-22-22-20000000000000000
χ422222-2-2-2-22222-2-2-2-222-2-20000000022-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000-22-22-22-220000000000000000
χ432222-2-2-2-22222-2-2-2-222-2-20000000022-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000002-22-2-22-220000000000000000
χ442222-2-2-2-22222-2-2-2-222-2-20000000022-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000-22-222-22-20000000000000000
χ452222-2-2-2-2-2-2-2-22222-2-2220000000022-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ462222-2-2-2-2-2-2-2-22222-2-2220000000022-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ472222-2-2-2-2-2-2-2-22222-2-2220000000022-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ482222-2-2-2-2-2-2-2-22222-2-2220000000022-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4922-2-222-2-222-2-222-2-2000022-2-222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000002-2002-2002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5022-2-222-2-222-2-222-2-2000022-2-222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000-2200-2200-2200-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5122-2-222-2-222-2-222-2-2000022-2-222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000002-2002-2002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5222-2-222-2-222-2-222-2-2000022-2-222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000-2200-2200-2200-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5322-2-222-2-222-2-222-2-20000-2-222-2-2220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000002-2002-200-2200-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5422-2-222-2-222-2-222-2-20000-2-222-2-2220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000-2200-22002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5522-2-222-2-222-2-222-2-20000-2-222-2-2220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000002-2002-200-2200-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5622-2-222-2-222-2-222-2-20000-2-222-2-2220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000-2200-22002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5722-2-222-2-2-2-222-2-222000022-2-2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000002-200-22002-200-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ5822-2-222-2-2-2-222-2-222000022-2-2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000-22002-200-22002-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ5922-2-222-2-2-2-222-2-222000022-2-2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000002-200-22002-200-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ6022-2-222-2-2-2-222-2-222000022-2-2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000-22002-200-22002-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6122-2-222-2-2-2-222-2-2220000-2-22222-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000002-200-2200-22002-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ6222-2-222-2-2-2-222-2-2220000-2-22222-2-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000-22002-2002-200-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6322-2-222-2-2-2-222-2-2220000-2-22222-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000002-200-2200-22002-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6422-2-222-2-2-2-222-2-2220000-2-22222-2-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000-22002-2002-200-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ652-22-22-22-22i−2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−200002-2002i−2i002-2002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000000000000000
χ662-22-22-22-22i−2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000-2200−2i2i00-2200−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000000000000000
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χ1154-4-44-444-44i−4i−4i4i−4i4i4i−4i4i−4i−4i4i000000004-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-444-4−4i4i4i−4i4i−4i−4i4i−4i4i4i−4i000000004-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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