Finite Group Databasebeta

← Group #72260471

Character table — Group #72260471

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124
size1111222222222222222222222222224444444444444444444444444488888888888888888888888888888888888888888888161616161616161616161616161616163232323232323232
order1222224444444444448888161616161616161688888888888888161616161616161616161616888816161616161616163232323232323232323232323232323232323232323232323232323232323232224444448888888822448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ171111-1-1-1-1111111-1-1-1-1111111111111-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i1-11-1i−ii−i
χ181111-1-1-1-1111111-1-1-1-1111111111111-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii-11-11−ii−ii
χ191111-1-1-1-1111111-1-1-1-1111111111111-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i-11-11−ii−ii
χ201111-1-1-1-1111111-1-1-1-1111111111111-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1−i−iii−i−iii1-11-1i−ii−i
χ211111-1-1-1-1111111-1-1-1-1111111111111-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii1-11-1−ii−ii
χ221111-1-1-1-1111111-1-1-1-1111111111111-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i-11-11i−ii−i
χ231111-1-1-1-1111111-1-1-1-1111111111111-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−i−iii−i−iii-11-11i−ii−i
χ241111-1-1-1-1111111-1-1-1-1111111111111-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1ii−i−iii−i−i1-11-1−ii−ii
χ251111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1111-1-111-1-11
χ261111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-111-1-111-1
χ271111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111-111-1-111-1
χ281111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-11-1-111-1-11
χ291111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-11-1-11-111-1
χ301111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-111-11-1-11
χ311111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-111-11-1-11
χ321111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111-1-11-111-1
χ332222222222222222222222-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ342222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ35222222222222222222-2-2-2-200000000-2-2-2-222222222-2-2000000000000-2-2-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ36222222222222222222-2-2-2-200000000-2-2-2-222222222-2-2000000000000-2-2-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ37222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000022220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000000000000000
χ38222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000222200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000000000000000
χ3922222222-2-2-2-222-2-2-2-222222222222222-2-22i2i2i2i−2i−2i−2i−2i-2-2-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-222222222222222-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-2222i2i2i2i−2i−2i−2i−2i22000000000000−2i−2i2i2i0000000022−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4222222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-2222i2i2i2i−2i−2i−2i−2i22000000000000−2i−2i2i2i00000000−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4322222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-222−2i−2i−2i−2i2i2i2i2i220000000000002i2i−2i−2i0000000022−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4422222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-222−2i−2i−2i−2i2i2i2i2i220000000000002i2i−2i−2i00000000−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i-2-22222-2-2-2-222222i−2i2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i-2-22222-2-2-2-22222−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-2-2-20000000022-2-22i2i−2i−2i2i2i−2i−2i22000000000000−2i2i−2i2i0000000022−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-2-2-20000000022-2-22i2i−2i−2i2i2i−2i−2i22000000000000−2i2i−2i2i00000000−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ492222-2-2-2-2222222-2-2-2-2-2-2-2-20000000022-2-2−2i−2i2i2i−2i−2i2i2i220000000000002i−2i2i−2i0000000022−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ502222-2-2-2-2222222-2-2-2-2-2-2-2-20000000022-2-2−2i−2i2i2i−2i−2i2i2i220000000000002i−2i2i−2i00000000−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ512222-2-2-2-2-2-2-2-2222222222222222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22-2-22-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ522222-2-2-2-2-2-2-2-2222222222222222222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2-222-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-200000000222222-2-2-2-222-2-2000000000000-222-20000000022−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−2000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-2-2-200000000222222-2-2-2-222-2-2000000000000-222-200000000−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−222000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222222-2-2-2-2000000002222-2-22222-2-2-2-20000000000002-2-220000000022−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−222000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222222-2-2-2-2000000002222-2-22222-2-2-2-20000000000002-2-2200000000−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−2000000000000000000000000
χ5722-2-22-22-22i−2i2i−2i2-22i−2i2i−2i0000i2i2i2i2−i2−i2−i2−i200002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60022−2−222−2−2i2i2−i2−i200001+i−1−i1+i−1−i1−i−1+i1−i−1+iζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000000000000000
χ5822-2-22-22-22i−2i2i−2i2-22i−2i2i−2i0000i2i2i2i2−i2−i2−i2−i200002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60022−2−222−2−2i2i2−i2−i200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.