Finite Group Databasebeta

← Group #10815961

Character table — Group #10815961

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222444444444444444444444444444444444466666666888888881212121212121212121212121212121212121212161616161616161624242424
order1222444422344444444446668888121212126688888812121212121212121212242424242424242424242424242424242244888824448888222444444488888888886121212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1111111111111-1-11111-1-1-1-11-1-11-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-11-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-1111111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-111-111-1-1-1-11111111111-111-111-1-1-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ1011111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-111-1-1-1111-1-11-1-1-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-1
χ1111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1111111111-1-1111-1-111-1-1
χ1211111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111-1111111-1-1-1-1-1-11111-111-1-1-111-1-111
χ1311111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ1411111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ1511111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ171111-1-1-1-1-1-11iiii−i−i−i−i11111ii−i−i-1-1-1-1-1-1i−i11-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i11-1-1i−ii−i-1111-1-1ii−i−ii−iii−i−i11-1-111-1-1i−ii−i1-1i−i
χ181111-1-1-1-1-1-11iiii−i−i−i−i11111ii−i−i-1-1-1-1-1-1i−i11-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i-1-111−ii−ii-1-1-1111ii−i−ii−i−i−iii11-1-1-1-111−ii−ii-11−ii
χ191111-1-1-1-1-1-11iiii−i−i−i−i11111ii−i−i-1-1-1-1-1-1i−i11-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii11-1-1i−ii−i1-1-1-111−i−iii−ii−i−iii-1-11111-1-1i−ii−i-11−ii
χ201111-1-1-1-1-1-11iiii−i−i−i−i11111ii−i−i-1-1-1-1-1-1i−i11-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-1-111−ii−ii111-1-1-1−i−iii−iiii−i−i-1-111-1-111−ii−ii1-1i−i
χ211111-1-1-1-1-1-11iiii−i−i−i−i11111−i−iii-1-1-1-1-1-1−ii-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii1-11-1−iii−i-1111-1-1ii−i−i−iiii−i−i-1-1111-11-1−iii−i-11−ii
χ221111-1-1-1-1-1-11iiii−i−i−i−i11111−i−iii-1-1-1-1-1-1−ii-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-11-11i−i−ii-1-1-1111ii−i−i−ii−i−iii-1-111-11-11i−i−ii1-1i−i
χ231111-1-1-1-1-1-11iiii−i−i−i−i11111−i−iii-1-1-1-1-1-1−ii-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i1-11-1−iii−i1-1-1-111−i−iiii−i−i−iii11-1-11-11-1−iii−i1-1i−i
χ241111-1-1-1-1-1-11iiii−i−i−i−i11111−i−iii-1-1-1-1-1-1−ii-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i-11-11i−i−ii111-1-1-1−i−iiii−iii−i−i11-1-1-11-11i−i−ii-11−ii
χ251111-1-1-1-1-1-11−i−i−i−iiiii11111ii−i−i-1-1-1-1-1-1i−i-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i1-11-1i−i−ii-1111-1-1−i−iiii−i−i−iii-1-1111-11-1i−i−ii-11i−i
χ261111-1-1-1-1-1-11−i−i−i−iiiii11111ii−i−i-1-1-1-1-1-1i−i-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-11-11−iii−i-1-1-1111−i−iiii−iii−i−i-1-111-11-11−iii−i1-1−ii
χ271111-1-1-1-1-1-11−i−i−i−iiiii11111ii−i−i-1-1-1-1-1-1i−i-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111-1-111−i−iii1-11-1i−i−ii1-1-1-111ii−i−i−iiii−i−i11-1-11-11-1i−i−ii1-1−ii
χ281111-1-1-1-1-1-11−i−i−i−iiiii11111ii−i−i-1-1-1-1-1-1i−i-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111-1-111−i−iii-11-11−iii−i111-1-1-1ii−i−i−ii−i−iii11-1-1-11-11−iii−i-11i−i
χ291111-1-1-1-1-1-11−i−i−i−iiiii11111−i−iii-1-1-1-1-1-1−ii11-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii11-1-1−ii−ii-1111-1-1−i−iii−ii−i−iii11-1-111-1-1−ii−ii1-1−ii
χ301111-1-1-1-1-1-11−i−i−i−iiiii11111−i−iii-1-1-1-1-1-1−ii11-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii-1-111i−ii−i-1-1-1111−i−iii−iiii−i−i11-1-1-1-111i−ii−i-11i−i
χ311111-1-1-1-1-1-11−i−i−i−iiiii11111−i−iii-1-1-1-1-1-1−ii11-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i11-1-1−ii−ii1-1-1-111ii−i−ii−iii−i−i-1-11111-1-1−ii−ii-11i−i
χ321111-1-1-1-1-1-11−i−i−i−iiiii11111−i−iii-1-1-1-1-1-1−ii11-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-1-111i−ii−i111-1-1-1ii−i−ii−i−i−iii-1-111-1-111i−ii−i1-1−ii
χ332222222222-12222222222-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222222200000000000000000000-1-1-1-1-1-1-1-10000
χ342222222222-12222222222-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-200000000000000000000111111110000
χ352222222222-12222222222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000002-2-22-2-22200000000000000000000-111-111-1-10000
χ362222222222-12222222222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000-222-222-2-2000000000000000000001-1-11-1-1110000
χ372222222222-1-2-2-2-2-2-2-2-222-1-1-12222-1-1-1-1-1-122-2-2-2-2-111111111-1-1-1-1-1-1-1-1-111111111000000002-2-2222-2-200000000000000000000-111-1-1-1110000
χ382222222222-1-2-2-2-2-2-2-2-222-1-1-12222-1-1-1-1-1-122-2-2-2-2-111111111-1-1-1-1-1-1-1-1-11111111100000000-222-2-2-222000000000000000000001-1-1111-1-10000
χ392222222222-1-2-2-2-2-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-111111111-111111111-1-1-1-1-1-1-1-1000000002222-2-2-2-200000000000000000000-1-1-1-111110000
χ402222222222-1-2-2-2-2-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-111111111-111111111-1-1-1-1-1-1-1-100000000-2-2-2-22222000000000000000000001111-1-1-1-10000
χ4122222222-2-2200000000-2-222222222222-2-2-2-20000-200000000-222-2-222-2-2000000002222222200000000-200-2000000-2-200000000000000000000
χ4222222222-2-2200000000-2-222222222222-2-2-2-20000-200000000-222-2-222-2-200000000-2-2-2-2-2-2-2-20000000020020000002200000000000000000000
χ4322222222-2-2200000000-2-2222-2-2-2-22222-2-2220000-200000000-2-2-222-2-222000000002222-2-2-2-200000000-200-20000002200000000000000000000
χ4422222222-2-2200000000-2-2222-2-2-2-22222-2-2220000-200000000-2-2-222-2-22200000000-2-2-2-22222000000002002000000-2-200000000000000000000
χ452222-2-2-2-222200000000-2-22222i2i−2i−2i-2-2-2-222−2i2i0000-200000000-22i2i−2i−2i−2i−2i2i2i0000000022-2-22i2i−2i−2i00000000200-2000000−2i2i00000000000000000000
χ462222-2-2-2-222200000000-2-22222i2i−2i−2i-2-2-2-222−2i2i0000-200000000-22i2i−2i−2i−2i−2i2i2i00000000-2-222−2i−2i2i2i00000000-20020000002i−2i00000000000000000000
χ472222-2-2-2-222200000000-2-2222−2i−2i2i2i-2-2-2-2222i−2i0000-200000000-2−2i−2i2i2i2i2i−2i−2i0000000022-2-2−2i−2i2i2i00000000200-20000002i−2i00000000000000000000
χ482222-2-2-2-222200000000-2-2222−2i−2i2i2i-2-2-2-2222i−2i0000-200000000-2−2i−2i2i2i2i2i−2i−2i00000000-2-2222i2i−2i−2i00000000-2002000000−2i2i00000000000000000000
χ492222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-12i2i−2i−2i1111112i−2i22-2-2-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-111110000000022-2-22i−2i2i−2i00000000000000000000-1-111−ii−ii0000
χ502222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-12i2i−2i−2i1111112i−2i22-2-2-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-1111100000000-2-222−2i2i−2i2i0000000000000000000011-1-1i−ii−i0000
χ512222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-1−2i−2i2i2i111111−2i2i-2-222-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-1000000002-22-2−2i2i2i−2i00000000000000000000-11-11i−i−ii0000
χ522222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-1−2i−2i2i2i111111−2i2i-2-222-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-100000000-22-222i−2i−2i2i000000000000000000001-11-1−iii−i0000
χ532222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-12i2i−2i−2i1111112i−2i-2-222-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-1000000002-22-22i−2i−2i2i00000000000000000000-11-11−iii−i0000
χ542222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-12i2i−2i−2i1111112i−2i-2-222-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-100000000-22-22−2i2i2i−2i000000000000000000001-11-1i−i−ii0000
χ552222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-1−2i−2i2i2i111111−2i2i22-2-2-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-111110000000022-2-2−2i2i−2i2i00000000000000000000-1-111i−ii−i0000
χ562222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-1−2i−2i2i2i111111−2i2i22-2-2-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-1111100000000-2-2222i−2i2i−2i0000000000000000000011-1-1−ii−ii0000
χ5722-2-22i−2i2i−2i0021+i1+i−1−i−1−i1−i1−i−1+i−1+i002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i00002−2−i2i201+i1+i−1−i−1−i1−i1−i−1+i−1+i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130022−2−2−i2−i2i2i22-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000001+i−1−i1−i−1+i0000002−2−i2i2000000000000
χ5822-2-22i−2i2i−2i0021+i1+i−1−i−1−i1−i1−i−1+i−1+i002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i00002−2−i2i201+i1+i−1−i−1−i1−i1−i−1+i−1+i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130022−2−2−i2−i2i2i2-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−1−i1+i−1+i1−i000000−22i2−i2000000000000
χ5922-2-22i−2i2i−2i0021+i1+i−1−i−1−i1−i1−i−1+i−1+i002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i0000−22i2−i201+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−2−222i2i2−i2−i22-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000001+i−1−i1−i−1+i000000−22i2−i2000000000000
χ6022-2-22i−2i2i−2i0021+i1+i−1−i−1−i1−i1−i−1+i−1+i002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i0000−22i2−i201+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−2−222i2i2−i2−i2-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i1+i−1+i1−i0000002−2−i2i2000000000000
χ6122-2-22i−2i2i−2i002−1−i−1−i1+i1+i−1+i−1+i1−i1−i002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i0000−22i2−i20−1−i−1−i1+i1+i−1+i−1+i1−i1−i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−2−222i2i2−i2−i22-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i1+i−1+i1−i000000−22i2−i2000000000000
χ6222-2-22i−2i2i−2i002−1−i−1−i1+i1+i−1+i−1+i1−i1−i002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i0000−22i2−i20−1−i−1−i1+i1+i−1+i−1+i1−i1−i02ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−2−222i2i2−i2−i2-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000001+i−1−i1−i−1+i0000002−2−i2i2000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.