Finite Group Databasebeta

← Group #72321676

Character table — Group #72321676

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1122222222222224444444444444444488888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232323232326464646464646464
order12222444488161616164444888888816161616161688888888161616163232323232323232323232323232323216161616323232323232323264646464646464646464646464646464646464646464646464646464646464642222444488888888448816161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111111-1-1-1-111-1-11-1-1111111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1ii−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
χ10111111111111111-1-1-1-111-1-11-1-1111111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1ii−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
χ11111111111111111-1-1-1-111-1-11-1-1111111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1ii−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
χ12111111111111111-1-1-1-111-1-11-1-1111111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1ii−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
χ13111111111111111-1-1-1-111-1-11-1-1111111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1−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
χ14111111111111111-1-1-1-111-1-11-1-1111111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1−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
χ15111111111111111-1-1-1-111-1-11-1-1111111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1−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
χ16111111111111111-1-1-1-111-1-11-1-1111111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1−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
χ17111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−iζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6iiii−i−i−i−i1111-1-1-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ211-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−i1-1ζ6−ζ6ζ2−ζ2
χ18111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−iζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6iiii−i−i−i−i1111-1-1-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ii-11−ζ6ζ6−ζ2ζ2
χ19111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−iζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−i−i−i−iiiii-1-1-1-11111−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ211-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ii-11−ζ6ζ6−ζ2ζ2
χ20111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−iζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−i−i−i−iiiii-1-1-1-11111−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−i1-1ζ6−ζ6ζ2−ζ2
χ21111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6iiii−i−i−i−i1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ211-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−i1-1−ζ6ζ6−ζ2ζ2
χ22111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6iiii−i−i−i−i1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ii-11ζ6−ζ6ζ2−ζ2
χ23111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−i−i−i−iiiii-1-1-1-11111ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ211-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ii-11ζ6−ζ6ζ2−ζ2
χ24111-1-1-11-1111-1-1-1-1i−ii−i1-1i−i-1i−i1111-1-1−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6i−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−i−i−i−iiiii-1-1-1-11111ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6i−i1-1−ζ6ζ6−ζ2ζ2
χ25111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii−ii11-1-1−i−iii11-1-1−i−iiiζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2iiii−i−i−i−i-1-1-1-11111−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ611-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2i−i-11−ζ2ζ2−ζ6ζ6
χ26111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii−ii11-1-1−i−iii11-1-1−i−iiiζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2iiii−i−i−i−i-1-1-1-11111−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii1-1ζ2−ζ2ζ6−ζ6
χ27111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii−ii11-1-1−i−iii11-1-1−i−iiiζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−i−i−i−iiiii1111-1-1-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ611-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii1-1ζ2−ζ2ζ6−ζ6
χ28111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii−ii11-1-1−i−iii11-1-1−i−iiiζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−i−i−i−iiiii1111-1-1-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2i−i-11−ζ2ζ2−ζ6ζ6
χ29111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2iiii−i−i−i−i-1-1-1-11111ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ611-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2i−i-11ζ2−ζ2ζ6−ζ6
χ30111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2iiii−i−i−i−i-1-1-1-11111ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ii1-1−ζ2ζ2−ζ6ζ6
χ31111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−i−i−i−iiiii1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ611-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii1-1−ζ2ζ2−ζ6ζ6
χ32111-1-1-11-1111-1-1-1-1−ii−ii1-1−ii-1−ii1111-1-1−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−i−i−i−iiiii1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2i−i-11ζ2−ζ2ζ6−ζ6
χ3322222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ3422222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ35222222222222222-2-2-2-222-2-22-2-22222222i2i2i2i−2i−2i−2i−2i-2-2-2-2-2-2-2-22222-2-2-2-222222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ36222222222222222-2-2-2-222-2-22-2-2222222−2i−2i−2i−2i2i2i2i2i-2-2-2-2-2-2-2-22222-2-2-2-22222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ3722222222222-2-2-2-222222222222-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-2-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ3822222222222-2-2-2-222222222222-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-2-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ3922222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000000000000000
χ4022222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000000000000000
χ4122222222222-2-2-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i22220000000000000000−2i−2i2i2i0000000022−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4222222222222-2-2-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i22220000000000000000−2i−2i2i2i00000000−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4322222222222-2-2-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i222200000000000000002i2i−2i−2i0000000022−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4422222222222-2-2-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i222200000000000000002i2i−2i−2i00000000−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ45222-2-2-22-222222222i−2i2i−2i2-22i−2i-22i−2i-2-2-2-2222ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6−2i2i−2i2i0000000000000000−2ζ22ζ2−2ζ62ζ600000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000
χ46222-2-2-22-222222222i−2i2i−2i2-22i−2i-22i−2i-2-2-2-2222ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6−2i2i−2i2i0000000000000000−2ζ22ζ2−2ζ62ζ600000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−21−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000
χ47222-2-2-22-222222222i−2i2i−2i2-22i−2i-22i−2i-2-2-2-222−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6−2i2i−2i2i00000000000000002ζ2−2ζ22ζ6−2ζ600000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2221−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000
χ48222-2-2-22-222222222i−2i2i−2i2-22i−2i-22i−2i-2-2-2-222−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6−2i2i−2i2i00000000000000002ζ2−2ζ22ζ6−2ζ600000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.