Finite Group Databasebeta

← Group #72319441

Character table — Group #72319441

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11112222222222222222224444444444444444444444444444448888888888888888888888888888888888888888888832323232323232323232323232323232
order122222224444448888888824444488888888161616161616161616161616161616164488161616161616161632323232323232323232323232323232323232323232323232323232323232322444888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i111ii−i−i1iiiiii−i−i−i−i−i−iii−i−ii−ii−i1111-1-1-1-1ζζζζζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ311-1-1i−ii−iζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ10111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i111ii−i−i1iiiiii−i−i−i−i−i−iii−i−ii−ii−i1111-1-1-1-1ζζζζζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3-1-111−ii−ii−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i111ii−i−i1iiiiii−i−i−i−i−i−iii−i−ii−ii−i1111-1-1-1-1−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζζζζ−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ311-1-1i−ii−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ12111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i111ii−i−i1iiiiii−i−i−i−i−i−iii−i−ii−ii−i1111-1-1-1-1−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζζζζ−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3-1-111−ii−iiζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ13111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii111−i−iii1−i−i−i−i−i−iiiiiii−i−iii−ii−ii1111-1-1-1-1ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζζζζζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ11-1-1−ii−iiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ14111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii111−i−iii1−i−i−i−i−i−iiiiiii−i−iii−ii−ii1111-1-1-1-1ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζζζζζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ-1-111i−ii−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ15111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii111−i−iii1−i−i−i−i−i−iiiiiii−i−iii−ii−ii1111-1-1-1-1−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζζζζ11-1-1−ii−ii−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ16111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii111−i−iii1−i−i−i−i−i−iiiiiii−i−iii−ii−ii1111-1-1-1-1−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζζζζ-1-111i−ii−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ171111-1-1111-1-111111-1-1-1-111-1-111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1111-11-11-11-1
χ181111-1-1111-1-111111-1-1-1-111-1-111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-1-11-11-11-11
χ191111-1-1111-1-111111-1-1-1-111-1-111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-111-11-11-11-11
χ201111-1-1111-1-111111-1-1-1-111-1-111111-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-111-1-11-11-11-11-1
χ211111-1-1111-1-111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1i−ii−i−ii−ii
χ221111-1-1111-1-111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1-1-111−ii−iii−ii−i
χ231111-1-1111-1-111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1−ii−iii−ii−i
χ241111-1-1111-1-111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1-1-111i−ii−i−ii−ii
χ251111-1-1-1-11-1-11-1-1-1-11111-1-111ii−i−i1-1-1ii−i−i1ii−i−i−i−i−i−iiiiiii−i−i−ii−ii11-1-1-1-111ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-11-1−iii−iζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ261111-1-1-1-11-1-11-1-1-1-11111-1-111ii−i−i1-1-1ii−i−i1ii−i−i−i−i−i−iiiiiii−i−i−ii−ii11-1-1-1-111ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11-11i−i−ii−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ271111-1-1-1-11-1-11-1-1-1-11111-1-111ii−i−i1-1-1ii−i−i1ii−i−i−i−i−i−iiiiiii−i−i−ii−ii11-1-1-1-111−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-11-1−iii−i−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ281111-1-1-1-11-1-11-1-1-1-11111-1-111ii−i−i1-1-1ii−i−i1ii−i−i−i−i−i−iiiiiii−i−i−ii−ii11-1-1-1-111−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11-11i−i−iiζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ291111-1-1-1-11-1-11-1-1-1-11111-1-111−i−iii1-1-1−i−iii1−i−iiiiiii−i−i−i−i−i−iiii−ii−i11-1-1-1-111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζ1-11-1i−i−iiζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ301111-1-1-1-11-1-11-1-1-1-11111-1-111−i−iii1-1-1−i−iii1−i−iiiiiii−i−i−i−i−i−iiii−ii−i11-1-1-1-111ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζ-11-11−iii−i−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ311111-1-1-1-11-1-11-1-1-1-11111-1-111−i−iii1-1-1−i−iii1−i−iiiiiii−i−i−i−i−i−iiii−ii−i11-1-1-1-111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ1-11-1i−i−ii−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ321111-1-1-1-11-1-11-1-1-1-11111-1-111−i−iii1-1-1−i−iii1−i−iiiiiii−i−i−i−i−i−iiii−ii−i11-1-1-1-111−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζ-11-11−iii−iζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ33222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2222-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3522222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000022-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ3622222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000022-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ3722222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-22222-20000000000000000-2-22200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-22222-20000000000000000-2-22200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ39222222-2-22222-2-222222222-2-22i2i−2i−2i-2-2-2−2i−2i2i2i-200000000000000002i−2i−2i2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000
χ40222222-2-22222-2-222222222-2-22i2i−2i−2i-2-2-2−2i−2i2i2i-200000000000000002i−2i−2i2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000
χ41222222-2-22222-2-222222222-2-2−2i−2i2i2i-2-2-22i2i−2i−2i-20000000000000000−2i2i2i−2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ42222222-2-22222-2-222222222-2-2−2i−2i2i2i-2-2-22i2i−2i−2i-20000000000000000−2i2i2i−2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ43222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22i2i−2i−2i2222i2i−2i−2i2−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i2i2i2i−2i2i−2i-2-2-2-22222000000000000000000000000000000000000000000000000
χ44222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2−2i−2i2i2i222−2i−2i2i2i22i2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i−2i−2i2i−2i2i-2-2-2-22222000000000000000000000000000000000000000000000000
χ452222-2-2222-2-222222-2-2-2-222-2-222222-2-222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ462222-2-2222-2-222222-2-2-2-222-2-2-2-2-2-22-2-2-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-222-2-222000000000000000000000000000000000000000000000000
χ472222-2-2222-2-2222-2-22222-2-2-2-22222-222-2-2-2-2-20000000000000000-2-2220000000022−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2220000000000000000
χ482222-2-2222-2-2222-2-22222-2-2-2-22222-222-2-2-2-2-20000000000000000-2-22200000000−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−20000000000000000
χ492222-2-2222-2-2222-2-22222-2-2-2-2-2-2-2-2-2222222-2000000000000000022-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ502222-2-2222-2-2222-2-22222-2-2-2-2-2-2-2-2-2222222-2000000000000000022-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ512222-2-2-2-22-2-22-2-222-2-2-2-222222i2i−2i−2i-222−2i−2i2i2i-20000000000000000−2i2i2i−2i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ522222-2-2-2-22-2-22-2-222-2-2-2-222222i2i−2i−2i-222−2i−2i2i2i-20000000000000000−2i2i2i−2i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ532222-2-2-2-22-2-22-2-222-2-2-2-22222−2i−2i2i2i-2222i2i−2i−2i-200000000000000002i−2i−2i2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ542222-2-2-2-22-2-22-2-222-2-2-2-22222−2i−2i2i2i-2222i2i−2i−2i-200000000000000002i−2i−2i2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ552222-2-2-2-22-2-22-2-2-2-22222-2-2222i2i−2i−2i2-2-22i2i−2i−2i2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i−2i2i−2i2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-22-2-22-2-2-2-22222-2-222−2i−2i2i2i2-2-2−2i−2i2i2i22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i2i−2i2i−2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ572-2-22002-2-20022-2220000-2-2002i−2i2i−2i-2002i−2i2i−2i22i2i0000−2i−2i0000−2i−2i2i2i00002-2002-20000002ζ3−2ζ32ζ3−2ζ300002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ00002ζ−2ζ2ζ−2ζ0000000000000000
χ582-2-22002-2-20022-2220000-2-2002i−2i2i−2i-2002i−2i2i−2i22i2i0000−2i−2i0000−2i−2i2i2i00002-2002-2000000−2ζ32ζ3−2ζ32ζ30000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000−2ζ2ζ−2ζ2ζ0000000000000000
χ592-2-22002-2-20022-2220000-2-2002i−2i2i−2i-2002i−2i2i−2i2−2i−2i00002i2i00002i2i−2i−2i0000-2200-22002ζ−2ζ2ζ−2ζ00002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ300002ζ3−2ζ32ζ3−2ζ300000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.