Finite Group Databasebeta

← Group #72321314

Character table — Group #72321314

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124
size11112222222222222222222222444444444444444444444444444444444444444444444444888888888888888888888888888888888832323232323232323232323232323232
order12222244444444444488888888224444448888888888888888888888881616161616161616161616161616161688888888881616161616161616161616161616161616161616161616162224444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-111-1-1-1-1-11111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-111111-1-1-1-1
χ911111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11ii−i−i−i−iii
χ1411111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-111-1−i−iiiii−i−i
χ1511111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11−i−iiiii−i−i
χ1611111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-111-1ii−i−i−i−iii
χ171111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-111-11-11-11-1
χ181111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-11-1-11-11-11-11
χ191111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-111111-11-1-11-11-11-11-11-11
χ201111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-11-111-11-11-11-11-11-1
χ211111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-11-11-1-11-11
χ221111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111-11-111-11-1
χ231111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-11111-1-1-1-11-1-1111-1-1-11-111-11-1
χ241111-1-1-1-11111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1111-11-1-11-11
χ251111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-11111111111111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-11-11-1i−i−iii−i−ii
χ261111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-11111111111111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-11-11-11−iii−i−iii−i
χ271111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-11111111111111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-11-11-1−iii−i−iii−i
χ281111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-11111111111111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-11-11i−i−iii−i−ii
χ291111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-111i−i−ii−iii−i
χ301111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-111-1-1−iii−ii−i−ii
χ311111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11-1-111−iii−ii−i−ii
χ321111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-111-1-1i−i−ii−iii−i
χ33222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-222220000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-22222-2-2-2-20000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-200000000-2-2-222-2-220000000022-2-222-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ36222222222222-2-2-2-2-2-200000000-2-2-222-2-220000000022-2-222-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ37222222222222-2-2-2-2-2-200000000-2-2-222-2-2200000000-2-222-2-22200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ38222222222222-2-2-2-2-2-200000000-2-2-222-2-2200000000-2-222-2-22200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3922222222-2-2222222-2-222222222-2-22-2-2-22-2-2-2-2-2222222222222222222220000000000000000-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ4022222222-2-2222222-2-222222222-2-22-2-2-22-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2222222220000000000000000000000000000000000000000
χ4122222222-2-222-2-2-2-2220000000022-2-2-22-2-20000000022-2-222-2-2000000002222−2−2−2−2−2−2−2−22222000000-22-2222−2−2−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4222222222-2-222-2-2-2-2220000000022-2-2-22-2-20000000022-2-222-2-200000000−2−2−2−222222222−2−2−2−2000000-22-22−2−22222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4322222222-2-222-2-2-2-2220000000022-2-2-22-2-200000000-2-222-2-222000000002222−2−2−2−2−2−2−2−222220000002-22-222−2−2−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-222-2-2-2-2220000000022-2-2-22-2-200000000-2-222-2-22200000000−2−2−2−222222222−2−2−2−20000002-22-2−2−22222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ45222222-2-222-2-222-2-2222222-2-2-2-2-2-22-2-22-2222-2-222-2-2000000000000000000000000000000002-200000000000000002-22-22-22-22-22-22-22-20000000000000000
χ46222222-2-222-2-222-2-2222222-2-2-2-2-2-22-2-22-2222-2-222-2-2000000000000000000000000000000002-20000000000000000-22-22-22-22-22-22-22-220000000000000000
χ47222222-2-222-2-222-2-222-2-2-2-22222-2-22-2-22-22-2-222-2-222000000000000000022-2-222-2-222-2-222-2-2-22000000002-22-22-22-200000000000000000000000000000000
χ48222222-2-222-2-222-2-222-2-2-2-22222-2-22-2-22-22-2-222-2-2220000000000000000-2-222-2-222-2-222-2-222-2200000000-22-22-22-2200000000000000000000000000000000
χ49222222-2-222-2-2-2-222-2-20000000022-2-2-2-222000000000000000022-2-222-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2002-22-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ50222222-2-222-2-2-2-222-2-20000000022-2-2-2-222000000000000000022-2-222-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2002-22-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ51222222-2-222-2-2-2-222-2-20000000022-2-2-2-2220000000000000000-2-222-2-222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200-22-220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ52222222-2-222-2-2-2-222-2-20000000022-2-2-2-2220000000000000000-2-222-2-222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200-22-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ53222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222222-2-2-2-2-22222-2-200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ54222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222222-2-2-2-2-22222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ55222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-222-2-2-2-222000000000000000000000000000000002-200000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ56222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-222-2-2-2-222000000000000000000000000000000002-20000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ57222222-2-2-2-2-2-2-2-2222200000000-2-2-22222-2000000000000000022-2-222-2-222−2−2−2−222−2−22222−2−200-22-2200002−2−22−222−2−222−2−222−22−2−222−2−220000000000000000
χ58222222-2-2-2-2-2-2-2-2222200000000-2-2-22222-2000000000000000022-2-222-2-2−2−22222−2−222−2−2−2−22200-22-220000−222−22−2−222−2−222−2−22−222−2−222−20000000000000000
χ59222222-2-2-2-2-2-2-2-2222200000000-2-2-22222-20000000000000000-2-222-2-22222−2−2−2−222−2−22222−2−2002-22-200002−2−22−222−22−2−222−2−22−222−2−222−20000000000000000
χ60222222-2-2-2-2-2-2-2-2222200000000-2-2-22222-20000000000000000-2-222-2-222−2−22222−2−222−2−2−2−222002-22-20000−222−22−2−22−222−2−222−22−2−222−2−220000000000000000
χ612222-2-22222-2-222-2-2222222-2-2-2-2-22-2-22-22-222-2-2-2-22200000000000000000000000000000000-2200000000000000002-22-2-22-222-22-2-22-220000000000000000
χ622222-2-22222-2-222-2-2222222-2-2-2-2-22-2-22-22-222-2-2-2-22200000000000000000000000000000000-220000000000000000-22-222-22-2-22-222-22-20000000000000000
χ632222-2-22222-2-222-2-222-2-2-2-22222-22-2-22-22-2-2-22222-2-2000000000000000022-2-222-2-222-2-222-2-22-200000000-22-22-22-2200000000000000000000000000000000
χ642222-2-22222-2-222-2-222-2-2-2-22222-22-2-22-22-2-2-22222-2-20000000000000000-2-222-2-222-2-222-2-2222-2000000002-22-22-22-200000000000000000000000000000000
χ652222-2-22222-2-2-2-222-2-2000000002-22-222-2-2000000000000000022-2-2-2-222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2002-2-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
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χ672222-2-22222-2-2-2-222-2-2000000002-22-222-2-20000000000000000-2-22222-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200-222-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.