Finite Group Databasebeta

← Group #72225186

Character table — Group #72225186

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size111122222222224444444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161664646464646464646464646464646464
order12222244444444444444888888888888448816161616161616161616161616161616888888881616161616161616323232323232323232323232323232323232323232323232323232323232323222244488888816161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−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−iii−i−iii
χ111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ121111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ131111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−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−iii−i−iii
χ141111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ151111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ171111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31111-1-1-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-11-1i−ii−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ181111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31111-1-1-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11-11−ii−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ191111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-1-1-11111−i−i−i−iiiii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1-11i−i−iiζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ201111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-1-1-11111−i−i−i−iiiii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-111-1−iii−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ211111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-11-1i−ii−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ221111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11-11−ii−iiζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ231111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-1-1-11111−i−i−i−iiiiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1-11i−i−ii−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ241111-1-1111111-1-1-1-1i−ii−i11-1-1i−i11-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-1-1-11111−i−i−i−iiiiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-111-1−iii−iζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ251111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-11-1−ii−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ261111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11-11i−ii−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ271111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1-11−iii−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ281111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-111-1i−i−ii−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ291111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-11-1−ii−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ301111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11-11i−ii−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ311111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-1-1-11111iiii−i−i−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1-11−iii−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ321111-1-1111111-1-1-1-1−ii−ii11-1-1−ii11-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-1-1-11111iiii−i−i−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-111-1i−i−iiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ33222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ37222222-2-2-2-22222-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ38222222-2-2-2-22222-2-22222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ39222222-2-2-2-22222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ40222222-2-2-2-22222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ41222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ42222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ43222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222222222000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ44222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222222220000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ452222-2-2222222-2-2-2-22i−2i2i−2i22-2-22i−2i22-2-22i−2i2i−2i2i−2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000000000000000000000
χ462222-2-2222222-2-2-2-22i−2i2i−2i22-2-22i−2i22-2-22i−2i2i−2i2i−2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000000000000000000000
χ472222-2-2222222-2-2-2-2−2i2i−2i2i22-2-2−2i2i22-2-2−2i2i−2i2i−2i2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000000000000000000000000000
χ482222-2-2222222-2-2-2-2−2i2i−2i2i22-2-2−2i2i22-2-2−2i2i−2i2i−2i2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000000000000000000000000000
χ492222-2-2-2-2-2-222-2-2222i−2i2i−2i-2-2222i−2i22-2-22i−2i−2i2i−2i2i22-2-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ30000000000000000
χ502222-2-2-2-2-2-222-2-2222i−2i2i−2i-2-2222i−2i22-2-22i−2i−2i2i−2i2i22-2-2−2i−2i2i2i-2-2222i2i−2i−2i00000000000000000000000000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ30000000000000000
χ512222-2-2-2-2-2-222-2-2222i−2i2i−2i-2-2222i−2i22-2-22i−2i−2i2i−2i2i-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ522222-2-2-2-2-2-222-2-2222i−2i2i−2i-2-2222i−2i22-2-22i−2i−2i2i−2i2i-2-2222i2i−2i−2i22-2-2−2i−2i2i2i0000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-222−2i2i−2i2i-2-222−2i2i22-2-2−2i2i2i−2i2i−2i22-2-22i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ0000000000000000
χ542222-2-2-2-2-2-222-2-222−2i2i−2i2i-2-222−2i2i22-2-2−2i2i2i−2i2i−2i22-2-22i2i−2i−2i-2-222−2i−2i2i2i00000000000000000000000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ0000000000000000
χ552222-2-2-2-2-2-222-2-222−2i2i−2i2i-2-222−2i2i22-2-2−2i2i2i−2i2i−2i-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-222−2i2i−2i2i-2-222−2i2i22-2-2−2i2i2i−2i2i−2i-2-222−2i−2i2i2i22-2-22i2i−2i−2i0000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ572-2-222-200002-22-2002i−2i−2i2i00002i−2i2-22-2−2i2i000000002i−2i2i−2i2-22-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002-2002-2002i−2i002i−2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ582-2-222-200002-22-2002i−2i−2i2i00002i−2i2-22-2−2i2i000000002i−2i2i−2i2-22-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00-2200-2200−2i2i00−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.