Finite Group Databasebeta

← Group #72227047

Character table — Group #72227047

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112222222222244444444444444448888888888888888816161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323264646464
order12222444488884444448888888888444881616161616161616161616162244444488888888161632323232323232323232323232323232888888888888888888881616161632323232323232322488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-111-1-1
χ10111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i11−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-1-1-11111-1-111
χ11111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii11iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-1-1-11111-1-111
χ12111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-111-1-1
χ13111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−i1111-1-1-1-1-1-111
χ14111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i11−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-1-1-1111111-1-1
χ15111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii11iiiiiiii−i−i−i−i−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-1111111-1-1
χ16111111111111111-1-1-1-1111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii1111-1-1-1-1-1-111
χ17111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-11-11-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ31-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ311-1-1ii−i−i1-1i−i
χ18111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-11-11-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ31-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ3-1-111−i−iii-11−ii
χ19111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-11-11-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ3-1-111−i−iii-11−ii
χ20111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-11-11-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ311-1-1ii−i−i1-1i−i
χ21111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-1-11-11−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ31-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11−ii−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ−ζζ3−ζ311-1-1ii−i−i-11−ii
χ22111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-1-11-11−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ31-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11−ii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ−ζζ3−ζ3-1-111−i−iii1-1i−i
χ23111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-1-11-11−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1ζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11−iiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζζ−ζ3ζ3-1-111−i−iii1-1i−i
χ24111-1-111-1-1-1-1-1-111i−ii−i11-1i−i11-1i−i-1i−ii−i1-1ii−i−iii−i−i1-1-11-11−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11−iiζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζζ−ζ3ζ311-1-1ii−i−i-11−ii
χ25111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-11-11-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζ11-1-1−i−iii1-1−ii
χ26111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-11-11-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζ-1-111ii−i−i-11i−i
χ27111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-11-11-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζ-1-111ii−i−i-11i−i
χ28111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-11-11-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζ11-1-1−i−iii1-1−ii
χ29111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-1-11-11ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3−ζ3ζ−ζ11-1-1−i−iii-11i−i
χ30111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-1-11-11ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3−ζ3ζ−ζ-1-111ii−i−i1-1−ii
χ31111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-1-11-11ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3ζ3−ζζ-1-111ii−i−i1-1−ii
χ32111-1-111-1-1-1-1-1-111−ii−ii11-1−ii11-1−ii-1−ii−ii1-1−i−iii−i−iii1-1-11-11ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3ζ3−ζζ11-1-1−i−iii-11i−i
χ332222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2000000000000000000000000000000000000-2-2-2-2000000000000
χ342222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000002222000000000000
χ35222222222222222-2-2-2-2222-2-2222-2-22-2-2-2-2-2-222222222-2-2000000002i2i2i2i−2i−2i−2i−2i-2-2000000000000000000000000000000000000−2i−2i2i2i000000000000
χ36222222222222222-2-2-2-2222-2-2222-2-22-2-2-2-2-2-222222222-2-200000000−2i−2i−2i−2i2i2i2i2i-2-20000000000000000000000000000000000002i2i−2i−2i000000000000
χ37222222222-2-222-2-22222-2-2-22222222-2-2-2-2-2222222-2-2-2-2222222222200000000-2-20000000000000000-2-2-2-200000000000000000000000000000000
χ38222222222-2-222-2-22222-2-2-22222222-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-20000000000000000222200000000000000000000000000000000
χ39222222222-2-222-2-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000022000000000000000000002-22-22-22-2000000000000000000000000
χ40222222222-2-222-2-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000002200000000000000000000-22-22-22-22000000000000000000000000
χ41222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-2-2-2222222-2-2-2-22222222222-2-2-2-200000000-2-20000000000000000-2-22200000000000000000000000000000000
χ42222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-2-2-2222222-2-2-2-2222222-2-2-2-2222200000000-2-2000000000000000022-2-200000000000000000000000000000000
χ43222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-2-2-22222-2-22222-2-2-2-2-2-2000000000000000022000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ44222222222-2-222-2-2-2-2-2-2-2-2-2-2-2222-2-2-22222-2-22222-2-2-2-2-2-200000000000000002200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ45222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222-2-2000000000000000000002-22-22-22-20022−2−222−2−222−2−222−2−20000000000000000000000002−22−22−22−20000
χ46222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222-2-2000000000000000000002-22-22-22-200−2−222−2−222−2−222−2−222000000000000000000000000−22−22−22−220000
χ47222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222-2-200000000000000000000-22-22-22-220022−2−222−2−222−2−222−2−2000000000000000000000000−22−22−22−220000
χ48222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222-2-200000000000000000000-22-22-22-2200−2−222−2−222−2−222−2−2220000000000000000000000002−22−22−22−20000
χ49222222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000000000002−22−2−22−220000
χ50222222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2222-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000−22−222−22−20000
χ51222222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000−22−222−22−20000
χ52222222222-2-2-2-222-2-2-2-2-2-2-222-2-2-2222-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000000000002−22−2−22−220000
χ53222-2-222-2-22222222i−2i2i−2i-2-22−2i2i-2-22−2i2i-22i−2i−2i2i000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000000000002−2−22i2−i2−i2i20000
χ54222-2-222-2-22222222i−2i2i−2i-2-22−2i2i-2-22−2i2i-22i−2i−2i2i000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000−222−2−i2i2i2−i20000
χ55222-2-222-2-22222222i−2i2i−2i-2-22−2i2i-2-22−2i2i-22i−2i−2i2i00000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000−222−2−i2i2i2−i20000
χ56222-2-222-2-22222222i−2i2i−2i-2-22−2i2i-2-22−2i2i-22i−2i−2i2i00000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000000000002−2−22i2−i2−i2i20000
χ57222-2-222-2-2222222−2i2i−2i2i-2-222i−2i-2-222i−2i-2−2i2i2i−2i000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000−222−2i2−i2−i2i20000
χ58222-2-222-2-2222222−2i2i−2i2i-2-222i−2i-2-222i−2i-2−2i2i2i−2i000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000000000002−2−22−i2i2i2−i20000
χ59222-2-222-2-2222222−2i2i−2i2i-2-222i−2i-2-222i−2i-2−2i2i2i−2i00000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000000000002−2−22−i2i2i2−i20000
χ60222-2-222-2-2222222−2i2i−2i2i-2-222i−2i-2-222i−2i-2−2i2i2i−2i00000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000−222−2i2−i2−i2i20000
χ61222-2-222-2-222-2-2-2-22i−2i2i−2i-2-222i−2i22-22i−2i2−2i2i−2i2i2-22i2i−2i−2i−2i−2i2i2i2-22-22-22i2i−2i−2i00000000-220000000000000000-22−2i2i00000000000000000000000000000000
χ62222-2-222-2-222-2-2-2-22i−2i2i−2i-2-222i−2i22-22i−2i2−2i2i−2i2i2-22i2i−2i−2i−2i−2i2i2i2-2-22-22−2i−2i2i2i00000000-2200000000000000002-22i−2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.