Finite Group Databasebeta

← Group #72701

Character table — Group #72701

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111111112222222244444444444444444488881111111122222222444444444444444444888811111111222222224444444444444444448888
order1222444422444444444444444488888888444436661212121266121212121212121212121212121212122424242424242424121212123666121212126612121212121212121212121212121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-111111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-111111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-11111-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-111111-1-1-1-1-1-11111-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-111111-1-1-1-1-1-11111-1-11-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii1-1-111111-1-1-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii1-1-111111-1-1-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-111-11111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-111-11111-1-1-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-111-11111-1-1-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-111-11111-1-1-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i1-1-111111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i1-1-111111-1-1-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222-2-2-2-22222-2-20000000000000000000022222222-2-2-2-22222-2-20000000000000000000022222222-2-2-2-22222-2-200000000000000000000
χ1822222222-2-2-2-2-2-2-2-2220000000000000000000022222222-2-2-2-2-2-2-2-2220000000000000000000022222222-2-2-2-2-2-2-2-22200000000000000000000
χ192222-2-2-2-222-2-222-2-2-22000000000000000000002222-2-2-2-222-2-222-2-2-22000000000000000000002222-2-2-2-222-2-222-2-2-2200000000000000000000
χ202222-2-2-2-222-2-2-2-2222-2000000000000000000002222-2-2-2-222-2-2-2-2222-2000000000000000000002222-2-2-2-222-2-2-2-2222-200000000000000000000
χ2122-2-222-2-22-22-20000000000000000002-22-2000022-2-222-2-22-22-20000000000000000002-22-2000022-2-222-2-22-22-20000000000000000002-22-20000
χ2222-2-222-2-22-22-2000000000000000000-22-22000022-2-222-2-22-22-2000000000000000000-22-22000022-2-222-2-22-22-2000000000000000000-22-220000
χ2322-2-222-2-2-22-22000000000000002i−2i2i−2i0000000022-2-222-2-2-22-22000000000000002i−2i2i−2i0000000022-2-222-2-2-22-22000000000000002i−2i2i−2i00000000
χ2422-2-222-2-2-22-2200000000000000−2i2i−2i2i0000000022-2-222-2-2-22-2200000000000000−2i2i−2i2i0000000022-2-222-2-2-22-2200000000000000−2i2i−2i2i00000000
χ2522-2-2-2-2222-2-22000000000000002-2-220000000022-2-2-2-2222-2-22000000000000002-2-220000000022-2-2-2-2222-2-22000000000000002-2-2200000000
χ2622-2-2-2-2222-2-2200000000000000-222-20000000022-2-2-2-2222-2-2200000000000000-222-20000000022-2-2-2-2222-2-2200000000000000-222-200000000
χ2722-2-2-2-222-222-20000000000000000002i−2i−2i2i000022-2-2-2-222-222-20000000000000000002i−2i−2i2i000022-2-2-2-222-222-20000000000000000002i−2i−2i2i0000
χ2822-2-2-2-222-222-2000000000000000000−2i2i2i−2i000022-2-2-2-222-222-2000000000000000000−2i2i2i−2i000022-2-2-2-222-222-2000000000000000000−2i2i2i−2i0000
χ292-22-22i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000002-22-22i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000002-22-22i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ302-22-22i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000002-22-22i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000002-22-22i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ312-22-22i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000002-22-22i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000002-22-22i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ322-22-22i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000002-22-22i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000002-22-22i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ332-22-2−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000002-22-2−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000002-22-2−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ342-22-2−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000002-22-2−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000002-22-2−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ352-22-2−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000002-22-2−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000002-22-2−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ362-22-2−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000002-22-2−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000002-22-2−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ374-4-444i−4i−4i4i0000000000000000000000000000004-4-444i−4i−4i4i0000000000000000000000000000004-4-444i−4i−4i4i000000000000000000000000000000
χ384-4-44−4i4i4i−4i0000000000000000000000000000004-4-44−4i4i4i−4i0000000000000000000000000000004-4-44−4i4i4i−4i000000000000000000000000000000
χ3911111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ4011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ41111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ42111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ43111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ44111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ45111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ46111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ471111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32
χ481111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i−i−iii−i−iii-11-11−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ71−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ111+i32−1−i321+i32−1−i32
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χ1102-22-2−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000−1−i31+i3−1−i31+i3−2ζ112ζ11−2ζ112ζ110000−1−i31+i3−2ζ112ζ1100ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11000000000000−1+i31−i3−1+i31−i3−2ζ72ζ7−2ζ72ζ70000−1+i31−i3−2ζ72ζ700ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10000000000000
χ1112-22-2−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000−1−i31+i3−1−i31+i3−2ζ112ζ11−2ζ112ζ1100001+i3−1−i32ζ11−2ζ1100−ζ2−ζ11ζ2+ζ11−ζ2+ζ11ζ2−ζ11ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11000000000000−1+i31−i3−1+i31−i3−2ζ72ζ7−2ζ72ζ700001−i3−1+i32ζ7−2ζ700−ζ7−ζ10ζ7+ζ10ζ7−ζ10−ζ7+ζ10ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10000000000000
χ1122-22-2−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000−1−i31+i3−1−i31+i3−2ζ112ζ11−2ζ112ζ1100001+i3−1−i32ζ11−2ζ1100ζ2+ζ11−ζ2−ζ11ζ2−ζ11−ζ2+ζ11−ζ2−ζ11ζ2+ζ11−ζ2+ζ11ζ2−ζ11000000000000−1+i31−i3−1+i31−i3−2ζ72ζ7−2ζ72ζ700001−i3−1+i32ζ7−2ζ700ζ7+ζ10−ζ7−ζ10−ζ7+ζ10ζ7−ζ10−ζ7−ζ10ζ7+ζ10ζ7−ζ10−ζ7+ζ10000000000000
χ1134-4-444i−4i−4i4i000000000000000000000000000000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ11−4ζ114ζ11000000000000000000000000000000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ7−4ζ74ζ7000000000000000000000000000000
χ1144-4-44−4i4i4i−4i000000000000000000000000000000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ114ζ11−4ζ11000000000000000000000000000000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ74ζ7−4ζ7000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.