Finite Group Databasebeta

← Group #123513

Character table — Group #123513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222222222222222222222222222222222222222222222444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1-1-111
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111
χ332222222222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-222-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-222-2-222-2-222-2-22-22-222-2-22-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ422222-2-2-2-22222-2-2-2-222-2-222-2-222-2-22-22-222-2-22-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ432222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222-22-22-2-222-22-220000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ442222-2-2-2-22222-2-2-2-222-2-222-2-2-2-222-22-22-2-222-22-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2-222-2-2-222-222-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ462222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2-222-2-2-222-222-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2222-2-2222-2-22-2-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2222-2-2222-2-22-2-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ492222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-22-2-22-2-2222-2-220000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ502222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-22-2-22-2-2222-2-22000000000000000000000000-222-2-222-200000000000000000000000000000000
χ512222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222-222-222-2-2-222-20000000000000000000000002-2-22-222-200000000000000000000000000000000
χ522222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222-222-222-2-2-222-2000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-22-2222-2-2-22-2200000000000000002-2-222-2-220000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2-22-2222-2-2-22-220000000000000000-222-2-222-20000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2222-22-2-2-2222-22-200000000000000002-2-22-222-20000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2222-22-2-2-2222-22-20000000000000000-222-22-2-220000000000000000000000000000000000000000
χ5722-2-222-2-222-2-222-2-22-22-22-22-22-22-2222-22-22-2-2-2-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5822-2-222-2-222-2-222-2-22-22-22-22-22-22-2222-22-22-2-2-2-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5922-2-222-2-222-2-222-2-22-22-22-22-2-22-22-2-2-22-22-22222-2000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ6022-2-222-2-222-2-222-2-22-22-22-22-2-22-22-2-2-22-22-22222-200000000000000000000000000000000-22-222-22-2000000000000000000000000
χ6122-2-222-2-222-2-222-2-2-22-22-22-222-22-2-2-22-2-22-2222-2200000000000000000000000000000000000000002-22-22-22-20000000000000000
χ6222-2-222-2-222-2-222-2-2-22-22-22-222-22-2-2-22-2-22-2222-220000000000000000000000000000000000000000-22-22-22-220000000000000000
χ6322-2-222-2-222-2-222-2-2-22-22-22-22-22-2222-222-22-2-2-22-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ6422-2-222-2-222-2-222-2-2-22-22-22-22-22-2222-222-22-2-2-22-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ6522-2-222-2-2-2-222-2-2222-22-2-22-222-22-222-22-22-22-2-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ6622-2-222-2-2-2-222-2-2222-22-2-22-222-22-222-22-22-22-2-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ6722-2-222-2-2-2-222-2-2222-22-2-22-22-22-22-2-22-22-22-222-22000000000000000000000000000000002-2-22-222-2000000000000000000000000
χ6822-2-222-2-2-2-222-2-2222-22-2-22-22-22-22-2-22-22-22-222-2200000000000000000000000000000000-222-22-2-22000000000000000000000000
χ6922-2-222-2-2-2-222-2-222-22-222-22-22-22-2-2-2-222-22-2222-200000000000000000000000000000000000000002-2-222-2-220000000000000000
χ7022-2-222-2-2-2-222-2-222-22-222-22-22-22-2-2-2-222-22-2222-20000000000000000000000000000000000000000-222-2-222-20000000000000000
χ7122-2-222-2-2-2-222-2-222-22-222-22-2-22-22222-2-22-22-2-2-2200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ7222-2-222-2-2-2-222-2-222-22-222-22-2-22-22222-2-22-22-2-2-220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ7322-2-2-2-22222-2-2-2-2222-2-222-2-222-2-222-2222-2-22-22-2-2000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ7422-2-2-2-22222-2-2-2-2222-2-222-2-222-2-222-2222-2-22-22-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ7522-2-2-2-22222-2-2-2-2222-2-222-2-22-222-2-22-2-2-222-22-222000000000000000000000000000000000000000000000000000000002-22-2-22-22
χ7622-2-2-2-22222-2-2-2-2222-2-222-2-22-222-2-22-2-2-222-22-22200000000000000000000000000000000000000000000000000000000-22-222-22-2
χ7722-2-2-2-22222-2-2-2-222-222-2-222-22-2-22-2222-222-22-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ7822-2-2-2-22222-2-2-2-222-222-2-222-22-2-22-2222-222-22-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ7922-2-2-2-22222-2-2-2-222-222-2-222-2-222-22-2-2-22-2-22-22220000000000000000000000000000000000000000000000002-22-2-22-2200000000
χ8022-2-2-2-22222-2-2-2-222-222-2-222-2-222-22-2-2-22-2-22-2222000000000000000000000000000000000000000000000000-22-222-22-200000000
χ8122-2-2-2-222-2-22222-2-22-2-22-222-22-2-222-2-2-2-222-2-2222000000000000000000000000000000000000000000000000000000002-2-222-2-22
χ8222-2-2-2-222-2-22222-2-22-2-22-222-22-2-222-2-2-2-222-2-222200000000000000000000000000000000000000000000000000000000-222-2-222-2
χ8322-2-2-2-222-2-22222-2-22-2-22-222-2-222-2-22222-2-222-2-2-2000000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ8422-2-2-2-222-2-22222-2-22-2-22-222-2-222-2-22222-2-222-2-2-200000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ8522-2-2-2-222-2-22222-2-2-222-22-2-222-2-22-22-2-22-2-222-2220000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ8622-2-2-2-222-2-22222-2-2-222-22-2-222-2-22-22-2-22-2-222-222000000000000000000000000000000000000000000000000-222-2-222-200000000
χ8722-2-2-2-222-2-22222-2-2-222-22-2-22-222-22-222-222-2-22-2-20000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ8822-2-2-2-222-2-22222-2-2-222-22-2-22-222-22-222-222-2-22-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ894-44-44-44-44-44-44-44-400000000000000000000000000000000004-4004-4000000000000000000000000000000000000000000000000
χ904-44-44-44-44-44-44-44-40000000000000000000000000000000000-4400-44000000000000000000000000000000000000000000000000
χ914-44-44-44-4-44-44-44-4400000000000000000000000000000000004-400-44000000000000000000000000000000000000000000000000
χ924-44-44-44-4-44-44-44-440000000000000000000000000000000000-44004-4000000000000000000000000000000000000000000000000
χ934-44-4-44-444-44-4-44-44000000000000000000000000000000004-4004-400000000000000000000000000000000000000000000000000
χ944-44-4-44-444-44-4-44-4400000000000000000000000000000000-4400-4400000000000000000000000000000000000000000000000000
χ954-44-4-44-44-44-444-44-4000000000000000000000000000000004-400-4400000000000000000000000000000000000000000000000000
χ964-44-4-44-44-44-444-44-400000000000000000000000000000000-44004-400000000000000000000000000000000000000000000000000
χ974-4-444-4-444-4-444-4-440000000000000000000000004-4004-40000000000000000000000000000000000000000000000000000000000
χ984-4-444-4-444-4-444-4-44000000000000000000000000-4400-440000000000000000000000000000000000000000000000000000000000
χ994-4-444-4-44-444-4-444-40000000000000000000000004-400-440000000000000000000000000000000000000000000000000000000000
χ1004-4-444-4-44-444-4-444-4000000000000000000000000-44004-40000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-44-4-44-444-4000000000000000000000000004-4004-400000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-44-4-44-444-400000000000000000000000000-4400-4400000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-4-444-44-4-44000000000000000000000000004-400-4400000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-4-444-44-4-4400000000000000000000000000-44004-400000000000000000000000000000000000000000000000000000000

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