Finite Group Databasebeta

← Group #72253361

Character table — Group #72253361

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222222224444444444444444888888888888888888161616161616161616161616161616161616161616161616161616161616161624242424242424242424242424242424242424242424242448484848
order122222222234444444466612121212222266666612121212121222444444446666121212124444668888121212121212121212121212121224242424242424242222222288888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ5111111111111111111111111111111111111111111-1-1111111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111111111111111111-1-1111111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ7111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911111111111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ1011111111111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ1111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1211111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1311111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1411111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ1511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ1611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ171-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-11-1ii−i−i1-11-111-1-111-1-11-1i−i1-1i−ii−iii−i−i1-111-1-1ii−i−iii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i1-1i−i
χ181-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-11-1ii−i−i1-11-111-1-111-1-11-1i−i1-1i−ii−iii−i−i1-111-1-1ii−i−iii−i−iii−i−i-1-111-1-111-1-111−i−iii−i−iii−i−iii-11−ii
χ191-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-11-1−i−iii1-11-111-1-111-1-11-1−ii1-1−ii−ii−i−iii1-111-1-1−i−iii−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−iii1-1−ii
χ201-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-11-1−i−iii1-11-111-1-111-1-11-1−ii1-1−ii−ii−i−iii1-111-1-1−i−iii−i−iii−i−iii-1-111-1-111-1-111ii−i−iii−i−iii−i−i-11i−i
χ211-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1-11i−i-11−ii−iiii−i−i-11-1-111ii−i−i−i−iii−i−iii11-1-111-1-1-1-111−i−iiiii−i−i−i−iii-11i−i
χ221-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1-11i−i-11−ii−iiii−i−i-11-1-111ii−i−i−i−iii−i−iii-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i1-1−ii
χ231-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1-11−ii-11i−ii−i−i−iii-11-1-111−i−iiiii−i−iii−i−i11-1-111-1-1-1-111ii−i−i−i−iiiii−i−i-11−ii
χ241-1-1111-1-11-1111-111-1-1-1-1-1111-1-111-1-111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1-11−ii-11i−ii−i−i−iii-11-1-111−i−iiiii−i−iii−i−i-1-111-1-11111-1-1−i−iiiii−i−i−i−iii1-1i−i
χ251-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-11-1ii−i−i-111-1-1-111-1-111-11−ii1-1−iii−iii−i−i1-1-1-111−i−iii−i−iiiii−i−i11-1-1-1-11111-1-1ii−i−i−i−iii−i−iii-11i−i
χ261-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-11-1ii−i−i-111-1-1-111-1-111-11−ii1-1−iii−iii−i−i1-1-1-111−i−iii−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−iii−i−i1-1−ii
χ271-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-11-1−i−iii-111-1-1-111-1-111-11i−i1-1i−i−ii−i−iii1-1-1-111ii−i−iii−i−i−i−iii11-1-1-1-11111-1-1−i−iiiii−i−iii−i−i-11−ii
χ281-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-11-1−i−iii-111-1-1-111-1-111-11i−i1-1i−i−ii−i−iii1-1-1-111ii−i−iii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iii−i−iii1-1i−i
χ291-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-1-11ii−i−i-11-11-1-111-1-1111-1−ii-11i−i−iiii−i−i-1111-1-1−i−iiiii−i−i−i−iii11-1-1-1-111-1-111−i−iii−i−iiiii−i−i1-1i−i
χ301-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-1-11ii−i−i-11-11-1-111-1-1111-1−ii-11i−i−iiii−i−i-1111-1-1−i−iiiii−i−i−i−iii-1-11111-1-111-1-1ii−i−iii−i−i−i−iii-11−ii
χ311-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-1-11−i−iii-11-11-1-111-1-1111-1i−i-11−iii−i−i−iii-1111-1-1ii−i−i−i−iiiii−i−i11-1-1-1-111-1-111ii−i−iii−i−i−i−iii1-1−ii
χ321-1-1111-1-11-1111-111-1-1-1-1-1111-1-1-1-11111-1-11-1111-1-1-1-11−i−iii-11-11-1-111-1-1111-1i−i-11−iii−i−i−iii-1111-1-1ii−i−i−i−iiiii−i−i-1-11111-1-111-1-1−i−iii−i−iiiii−i−i-11i−i
χ3322222222222-2-2-2-2-2-2-2-2222-2-2-2-22222222222-2-2-2-2-2-2000000-2-2002222-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i00002i−2i2i−2i0000
χ3422222222222-2-2-2-2-2-2-2-2222-2-2-2-22222222222-2-2-2-2-2-2000000-2-2002222-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000
χ3522222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000002200-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000
χ3622222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000002200-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i0000
χ372222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ382222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-122-2-2-1-1-2-2-2-21111-1-1-1-1-1-11111111111110000000000000000000000000000
χ392222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2222222-2-2-1-1-1-1-1-1-1-1-2-22211-2-2-2-2-1-1-1-1111111-1-1-1-1111111110000000000000000000000000000
χ402222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-211222211111111111111-1-1-1-1-1-1-1-10000000000000000000000000000
χ412222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1222222-2-22211111111-2-2-2-2-1-1-2-222-1-1-1-1-1-1111111111111-1-1-1-10000000000000000000000000000
χ422222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-22211111111-2-222-1-122-2-21111-1-11111-1-1-1-1-1-1-1-111110000000000000000000000000000
χ432222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-21111111122-2-21122-2-2-1-1-1-111-1-1-1-11111-1-1-1-111110000000000000000000000000000
χ442222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-211111111222211-2-222111111-1-1-1-1-1-1-1-11111-1-1-1-10000000000000000000000000000
χ4522222-2-2-2-2222-2-22-2-222222-2-2-2-200002-2-2-2-2222-22-22002-22-200000000000000000000002-22-200000000000000000000002-22-2000000002-22-200000000
χ4622222-2-2-2-2222-2-22-2-222222-2-2-2-200002-2-2-2-2222-22-22002-22-200000000000000000000002-22-20000000000000000000000-22-2200000000-22-2200000000
χ4722222-2-2-2-2222-2-22-2-222222-2-2-2-200002-2-2-2-2222-22-2200-22-220000000000000000000000-22-2200000000000000000000002-22-200000000-22-2200000000
χ4822222-2-2-2-2222-2-22-2-222222-2-2-2-200002-2-2-2-2222-22-2200-22-220000000000000000000000-22-220000000000000000000000-22-22000000002-22-200000000
χ492222-2-22-22-22-2-2-22222-2222-2-2-2-20000-2-22-22-22-22-22222000000-2-20000000000002200000000-2-200000000000000002-22-200002-22-20000000000000000
χ502222-2-22-22-22-2-2-22222-2222-2-2-2-20000-2-22-22-22-22-22222000000-2-20000000000002200000000-2-20000000000000000-22-220000-22-220000000000000000
χ512222-2-22-22-22-2-2-22222-2222-2-2-2-20000-2-22-22-22-22-222-2-200000022000000000000-2-2000000002200000000000000002-22-20000-22-220000000000000000
χ522222-2-22-22-22-2-2-22222-2222-2-2-2-20000-2-22-22-22-22-222-2-200000022000000000000-2-200000000220000000000000000-22-2200002-22-20000000000000000
χ532-2-2222-2-22-22-2-22-2-2222-2-22-2-22222-2-222-2-22-2-2-2-2222000000-220022-2-2-2-222000000000000000000000000000000000000000000002-2-2200002-2-220000
χ542-2-2222-2-22-22-2-22-2-2222-2-22-2-22222-2-222-2-22-2-2-2-2222000000-220022-2-2-2-22200000000000000000000000000000000000000000000-222-20000-222-20000
χ552-2-2222-2-22-22-2-22-2-2222-2-22-2-222-2-22222-2-22-2-2-2-22220000002-200-2-22222-2-2000000000000000000000000000000000000000000002-2-220000-222-20000
χ562-2-2222-2-22-22-2-22-2-2222-2-22-2-222-2-22222-2-22-2-2-2-22220000002-200-2-22222-2-200000000000000000000000000000000000000000000-222-200002-2-220000
χ572-2-2222-2-22-2-122-222-2-2-211-1-1-11122-2-2-1-111-11-1-1-11112-22i2i−2i−2i2-22-2-1-111-1-1112-22i−2i-112i−2i2i−2i−i−iii-11-1-111−i−iii−i−iii−i−iii0000000000000000000000000000
χ582-2-2222-2-22-2-122-222-2-2-211-1-1-11122-2-2-1-111-11-1-1-11112-2−2i−2i2i2i2-22-2-1-111-1-1112-2−2i2i-11−2i2i−2i2iii−i−i-11-1-111ii−i−iii−i−iii−i−i0000000000000000000000000000
χ592-2-2222-2-22-2-122-222-2-2-211-1-1-11122-2-2-1-111-11-1-1-1111-222i2i−2i−2i2-2-22-1-111-1-111-222i−2i1-1−2i2i−2i2i−i−iii1-111-1-1−i−iiiii−i−iii−i−i0000000000000000000000000000
χ602-2-2222-2-22-2-122-222-2-2-211-1-1-11122-2-2-1-111-11-1-1-1111-22−2i−2i2i2i2-2-22-1-111-1-111-22−2i2i1-12i−2i2i−2iii−i−i1-111-1-1ii−i−i−i−iii−i−iii0000000000000000000000000000
χ612-2-2222-2-22-2-122-222-2-2-211-1-1-111-2-222-1-111-11-1-1-11112-22i2i−2i−2i-222-211-1-111-1-1-22−2i2i-11−2i2i2i−2i−i−iii-1111-1-1ii−i−iii−i−i−i−iii0000000000000000000000000000
χ622-2-2222-2-22-2-122-222-2-2-211-1-1-111-2-222-1-111-11-1-1-11112-2−2i−2i2i2i-222-211-1-111-1-1-222i−2i-112i−2i−2i2iii−i−i-1111-1-1−i−iii−i−iiiii−i−i0000000000000000000000000000
χ632-2-2222-2-22-2-122-222-2-2-211-1-1-111-2-222-1-111-11-1-1-1111-222i2i−2i−2i-22-2211-1-111-1-12-2−2i2i1-12i−2i−2i2i−i−iii1-1-1-111ii−i−i−i−iiiii−i−i0000000000000000000000000000
χ642-2-2222-2-22-2-122-222-2-2-211-1-1-111-2-222-1-111-11-1-1-1111-22−2i−2i2i2i-22-2211-1-111-1-12-22i−2i1-1−2i2i2i−2iii−i−i1-1-1-111−i−iiiii−i−i−i−iii0000000000000000000000000000
χ652-2-222-222-2-222-222-22-2-2-2-22-2-22200002-222-2-222-2-22-2002i−2i−2i2i00000000000000000000002i−2i−2i2i00000000000000000000002-2-22000000002i−2i−2i2i00000000
χ662-2-222-222-2-222-222-22-2-2-2-22-2-22200002-222-2-222-2-22-2002i−2i−2i2i00000000000000000000002i−2i−2i2i0000000000000000000000-222-200000000−2i2i2i−2i00000000
χ672-2-222-222-2-222-222-22-2-2-2-22-2-22200002-222-2-222-2-22-200−2i2i2i−2i0000000000000000000000−2i2i2i−2i00000000000000000000002-2-2200000000−2i2i2i−2i00000000
χ682-2-222-222-2-222-222-22-2-2-2-22-2-22200002-222-2-222-2-22-200−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000000000000000000000-222-2000000002i−2i−2i2i00000000
χ692-2-22-2-2-22222-2-2222-2-22-2-22-2-2220000-2-2-22222-222-2-22-2000000-220000000000002-200000000-2200000000000000002-2-2200002-2-220000000000000000
χ702-2-22-2-2-22222-2-2222-2-22-2-22-2-2220000-2-2-22222-222-2-22-2000000-220000000000002-200000000-220000000000000000-222-20000-222-20000000000000000
χ712-2-22-2-2-22222-2-2222-2-22-2-22-2-2220000-2-2-22222-222-2-2-220000002-2000000000000-22000000002-200000000000000002-2-220000-222-20000000000000000
χ722-2-22-2-2-22222-2-2222-2-22-2-22-2-2220000-2-2-22222-222-2-2-220000002-2000000000000-22000000002-20000000000000000-222-200002-2-220000000000000000
χ734444444444-2-4-4-4-4-4-4-4-4-2-2-222224444-2-2-2-2-2-2222222000000-4-400-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ744444444444-2-4-4-4-4-4-4-4-4-2-2-22222-4-4-4-4-2-2-2-2-2-222222200000044002222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ7544444-4-4-4-444-444-444-4-4444444400004-4-4-4-44-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ7644444-4-4-4-44-24-4-44-4-444-2-2-222220000-22222-2-2-22-22-2004-44-40000000000000000000000-22-220000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).