Finite Group Databasebeta

← Group #72225218

Character table — Group #72225218

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size111111112222222222222222222222222222444444444444444444444444444444448888888888888888888888888888888888888888888888888888888816161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232323264646464
order12222222444444444444888888888888888844444444888888888888888888888888222222224444444488888888161616161616161616161616161616161616161616161616161616161616161644444444888888888888888822224444161616161616161616161616161616162244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ1211111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1311111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1411111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1511111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1611111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ171111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ181111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11−ii
χ191111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i-11−ii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-11−ii
χ201111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1-1i−i-11−ii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i
χ211111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-11−ii
χ221111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i
χ231111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ241111-1-1-1-1ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−ii−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-11−ii-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ251111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ261111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i
χ271111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1-1-111−i−iiiii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii-11i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-11i−i
χ281111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1-1-111−i−iiiii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1-1−ii-11i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii
χ291111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-11i−i
χ301111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii
χ311111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ321111-1-1-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−ii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-11i−i-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-11i−i
χ332222222222222222222222-2-222-2-222-2-222-2-22222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-200002222000022222-22-2-2-2-2-2000000000000000000000000000000000000222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ342222222222222222222222-2-222-2-222-2-222-2-22222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000-2-2-2-22-22-2-2-2-2-2000000000000000000000000000000000000-2-2-2-200000000222222220000000000000000000000000000
χ3522222222222222222222-2-222-2-222-2-222-2-22222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-22222000022220000-22-22-2-2-2-20000000000000000000000000000000022220000-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ3622222222222222222222-2-222-2-222-2-222-2-22222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000-22-22-2-2-2-200000000000000000000000000000000-2-2-2-2000022222222000000000000000000000000000000000000
χ3722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-22222000000000000000000000000000000000000000000000000000000002-22-22-22-200000000000000000000
χ3822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2222200000000000000000000000000000000000000000000000000000000-22-22-22-2200000000000000000000
χ392222222222222-22-22-22-200220022002200222-22-2-2-2-2-200-2-200-2-2002200220000000022220000222200000-20-200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2-2-2-2-200000000000000000000000000002−22−22−22−2000000000000
χ402222222222222-22-22-22-200220022002200222-22-2-2-2-2-200-2-200-2-2002200220000000022220000222200000-20-20000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222-2-2-2-20000000000000000000000000000−22−22−22−22000000000000
χ412222222222222-22-22-22-200220022002200222-22-2-2-2-2-200-2-200-2-20022002200000000-2-2-2-20000-2-2-2-200000-20-200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222220000000000000000000000000000−22−22−22−22000000000000
χ422222222222222-22-22-22-200220022002200222-22-2-2-2-2-200-2-200-2-20022002200000000-2-2-2-20000-2-2-2-200000-20-20000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222222200000000000000000000000000002−22−22−22−2000000000000
χ43222222222222-22-22-22-222200220022002200-22-22-2-2-2-2-2-200-2-20022002200000000000000222200002222-20-20000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000-2-2-2-2000000000000000000000000000000002−22−22−22−20000
χ44222222222222-22-22-22-222200220022002200-22-22-2-2-2-2-2-200-2-20022002200000000000000222200002222-20-200000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000-2-2-2-200000000000000000000000000000000−22−22−22−220000
χ45222222222222-22-22-22-222200220022002200-22-22-2-2-2-2-2-200-2-20022002200000000000000-2-2-2-20000-2-2-2-2-20-20000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000222200000000000000000000000000000000−22−22−22−220000
χ46222222222222-22-22-22-222200220022002200-22-22-2-2-2-2-2-200-2-20022002200000000000000-2-2-2-20000-2-2-2-2-20-200000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−22200002222000000000000000000000000000000002−22−22−22−20000
χ4722222222-2-2-2-22222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-222-2-222-2-2-2-2-2-2-2-2000022220000-2-2-2-2-22-22222200000000000000000000000000000000000022-2-200000000-2-2-2-222220000000000000000000000000000
χ4822222222-2-2-2-22222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-222-2-222-2-2-2-2-2-2-2-20000-2-2-2-200002222-22-222222000000000000000000000000000000000000-2-222000000002222-2-2-2-20000000000000000000000000000
χ4922222222-2-2-2-222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-222-2-222-2-22222-2-222-2-2-2-2-2-2-2-2-2-222220000-2-2-2-200002-22-222220000000000000000000000000000000022-2-20000-2-2-2-22222000000000000000000000000000000000000
χ5022222222-2-2-2-222222222-2-222-2-222-2-222-2-222-2-2-2-2-2-222-2-222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000222200002-22-2222200000000000000000000000000000000-2-22200002222-2-2-2-2000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.