Finite Group Databasebeta

← Group #72226957

Character table — Group #72226957

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616163232323232323232323232326464646464646464
order1222222244444444888888888888888844888888888888888816161616161616161616161616161616222222221616161616161616161616161616161616161616161616161616161616161616161616161616161644444444444488888888161616161616161616161616161616168888161616161616161622224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ71111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ911111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111
χ1011111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111111-1-1-1-111
χ1311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ1411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111
χ1511111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ171-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-11-11-1i−ii−ii−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i11-1-111-1-11-11-1i−ii−i
χ181-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-11-1-11i−i−iii−i−ii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−ii11-1-1-1-111-11-11−ii−ii
χ191-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-111-1−iii−i−iii−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i-1-11111-1-1-11-11−ii−ii
χ201-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-11-11−ii−ii−ii−ii-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−ii−ii-1-111-1-1111-11-1i−ii−i
χ211-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1111111111-11-1i−i−iii−i−ii11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii-1-111-1-1111-1-11i−i−ii
χ221-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1111111111-1-11i−ii−ii−ii−i11-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiii−ii−i-1-11111-1-1-111-1−iii−i
χ231-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-111-1−ii−ii−ii−ii-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii11-1-1-1-111-111-1−iii−i
χ241-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-11-11−iii−i−iii−i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i11-1-111-1-11-1-11i−i−ii
χ251-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1111111111-11-1−iii−i−iii−i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i-1-111-1-1111-1-11−iii−i
χ261-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1111111111-1-11−ii−ii−ii−ii11-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−ii−ii-1-11111-1-1-111-1i−i−ii
χ271-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-111111111-111-1i−ii−ii−ii−i-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i11-1-1-1-111-111-1i−i−ii
χ281-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-111111111-11-11i−i−iii−i−ii-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii11-1-111-1-11-1-11−iii−i
χ291-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11-11-1−ii−ii−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii11-1-111-1-11-11-1−ii−ii
χ301-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11-1-11−iii−i−iii−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i11-1-1-1-111-11-11i−ii−i
χ311-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-111-1i−i−iii−i−ii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii-1-11111-1-1-11-11i−ii−i
χ321-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-11-11i−ii−ii−ii−i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−ii−ii−i-1-111-1-1111-11-1−ii−ii
χ33222222222222222222-2-222-2-222-2-222-2-22222-2-2-2-2-2-222-2-2-2-2-2-20000000022222222000022220000222200000000-2-2-2-2-2-2-2-200000000000000000022002200220000-2-2-2-2000000000000000000-2-20000000000000000
χ34222222222222222222-2-222-2-222-2-222-2-22222-2-2-2-2-2-222-2-2-2-2-2-200000000222222220000-2-2-2-20000222200000000-2-2-2-2-2-2-2-2000000000000000000-2-200-2-200-2-200002222000000000000000000220000000000000000
χ35222222222222222222-2-222-2-222-2-222-2-22222-2-2-2-2-2-222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2000022220000-2-2-2-200000000222222220000000000000000002200-2-200-2-20000-2-2-2-2000000000000000000220000000000000000
χ36222222222222222222-2-222-2-222-2-222-2-22222-2-2-2-2-2-222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000-2-2-2-20000-2-2-2-20000000022222222000000000000000000-2-20022002200002222000000000000000000-2-20000000000000000
χ372222222222222222-2-222-2-222-2-222-2-22222-2-222-2-2-2-2-2-222-2-2-2-222222222000000002222000022220000-2-2-2-2-2-2-2-2000000000000000000000000220022002200-2-2-2-200000000000000000000-2-2000000000000000000
χ382222222222222222-2-222-2-222-2-222-2-22222-2-222-2-2-2-2-2-222-2-2-2-22222222200000000-2-2-2-2000022220000-2-2-2-2-2-2-2-2000000000000000000000000-2-200-2-200-2-20022220000000000000000000022000000000000000000
χ392222222222222222-2-222-2-222-2-222-2-22222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000-2-2-2-20000222222220000000000000000000000002200-2-200-2-200-2-2-2-20000000000000000000022000000000000000000
χ402222222222222222-2-222-2-222-2-222-2-22222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-20000-2-2-2-2000022222222000000000000000000000000-2-20022002200222200000000000000000000-2-2000000000000000000
χ41222222222-22-22-22-20022002200220022-2-200-2-2000000-2-200002222222222−2−222−2−222220000-2-2-2-22−22−20000000022−2−222−2−22222−2−2−2−22222−2−2−2−2-2-200-2-20022000000000022−2−222−2−20000000000002−22−2000000000000
χ42222222222-22-22-22-20022002200220022-2-200-2-2000000-2-200002222222222−2−222−2−2-2-2-2-20000-2-2-2-22−22−20000000022−2−222−2−22222−2−2−2−22222−2−2−2−222002200-2-20000000000−2−222−2−222000000000000−22−22000000000000
χ43222222222-22-22-22-20022002200220022-2-200-2-2000000-2-2000022222222−2−222−2−22222220000-2-2-2-2−22−2200000000−2−222−2−222−2−2−2−22222−2−2−2−22222-2-200-2-200220000000000−2−222−2−222000000000000−22−22000000000000
χ44222222222-22-22-22-20022002200220022-2-200-2-2000000-2-2000022222222−2−222−2−222-2-2-2-20000-2-2-2-2−22−2200000000−2−222−2−222−2−2−2−22222−2−2−2−2222222002200-2-2000000000022−2−222−2−20000000000002−22−2000000000000
χ45222222222-22-22-22-20022002200220022-2-200-2-2000000-2-20000-2-2-2-2-2-2-2-222−2−222−2−22222000022222−22−20000000022−2−222−2−2−2−2−2−22222−2−2−2−22222-2-2002200-2-2000000000022−2−222−2−2000000000000−22−22000000000000
χ46222222222-22-22-22-20022002200220022-2-200-2-2000000-2-20000-2-2-2-2-2-2-2-222−2−222−2−2-2-2-2-2000022222−22−20000000022−2−222−2−2−2−2−2−22222−2−2−2−222222200-2-200220000000000−2−222−2−2220000000000002−22−2000000000000
χ47222222222-22-22-22-20022002200220022-2-200-2-2000000-2-20000-2-2-2-2-2-2-2-2−2−222−2−222222200002222−22−2200000000−2−222−2−2222222−2−2−2−22222−2−2−2−2-2-2002200-2-20000000000−2−222−2−2220000000000002−22−2000000000000
χ48222222222-22-22-22-20022002200220022-2-200-2-2000000-2-20000-2-2-2-2-2-2-2-2−2−222−2−222-2-2-2-200002222−22−2200000000−2−222−2−2222222−2−2−2−22222−2−2−2−22200-2-20022000000000022−2−222−2−2000000000000−22−22000000000000
χ4922222222-22-22-22-222200220022002200-2-2-2-2000000-2-200000022−2−222−2−222222222000022222−22−2-2-2-2-222−2−222−2−20000000022−2−222−2−222−2−222−2−200-2-200-2-20022000000000000000022−2−222−2−2000000002−22−200000000
χ5022222222-22-22-22-222200220022002200-2-2-2-2000000-2-200000022−2−222−2−2222222220000-2-2-2-22−22−2-2-2-2-222−2−222−2−20000000022−2−222−2−222−2−222−2−20022002200-2-20000000000000000−2−222−2−22200000000−22−2200000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.