Finite Group Databasebeta

← Group #72323081

Character table — Group #72323081

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160
size112222222222222444444444444444444488888888888888888888888888888161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232326464646464646464646464646464646464646464128128128128
order1222244448816161616224444888888816161616161644488161616161616161632323232323232323232323232323232888888888161616161616323232323232323222224444161632323232323232326464646464646464646464646464646464646464646464646464646464646464222444888888888816161616481616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ81111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111111111-1-1-1-111-1-1
χ911111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i1-1i−i
χ1011111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111iiii−i−i−i−i−i−iii-11−ii
χ1111111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111-1-1-1-1-1-1-1-11111i−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−i−i−iiiii−i−iii-11−ii
χ1211111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111-1-1-1-1-1-1-1-11111i−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−i−i−iiiiiii−i−i1-1i−i
χ1311111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111-1-1-1-11111-1-1-1-1−ii−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−i−i−iiiii−i−iii1-1−ii
χ1411111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111-1-1-1-11111-1-1-1-1−ii−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−i−i−iiiiiii−i−i-11i−i
χ1511111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111-1-1-1-1-1-1-1-11111−ii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−iii−i−i-11i−i
χ1611111111111111111-1-1-1-1111-1-1-1-11111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111-1-1-1-1-1-1-1-11111−ii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1iiii−i−i−i−i−i−iii1-1−ii
χ17111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1
χ18111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ19111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-11111
χ20111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1111111-1-1-1-1
χ21111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1-1-111
χ22111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ23111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1111111-1-1
χ24111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111
χ25111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11ii−i−i−i−iii11ii−i−i-1-1-1-111111111-1-1-1-1−iiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iiiii−i−i-11−ii
χ26111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11ii−i−i−i−iii11ii−i−i-1-1-1-111111111-1-1-1-1−iiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii−i−iii1-1i−i
χ27111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11ii−i−i−i−iii11ii−i−i-1-1-1-11111-1-1-1-11111−iiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i−i−iii1-1i−i
χ28111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11ii−i−i−i−iii11ii−i−i-1-1-1-11111-1-1-1-11111−iiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−iii−i−i-11−ii
χ29111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−i−iiiii−i−i11−i−iii-1-1-1-111111111-1-1-1-1i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i−i−iii-11i−i
χ30111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−i−iiiii−i−i11−i−iii-1-1-1-111111111-1-1-1-1i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−iii−i−i1-1−ii
χ31111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−i−iiiii−i−i11−i−iii-1-1-1-11111-1-1-1-11111i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iiiii−i−i1-1−ii
χ32111111111111111-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11−i−iiiii−i−i11−i−iii-1-1-1-11111-1-1-1-11111i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii−i−iii-11i−i
χ3322222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-20000000022-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ3422222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222222200000000000000000000000000000000000000000000000000000000
χ3522222222222222222-2-2-2-2222-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222222222-22i2i2i2i−2i−2i−2i−2i-2-22i2i−2i−2i-2-2-2-22222000000002i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ3622222222222222222-2-2-2-2222-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2−2i−2i−2i−2i2i2i2i2i-2-2−2i−2i2i2i-2-2-2-2222200000000−2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ37222222222222222-2-222222222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222222222222200000000-2-2-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ38222222222222222-2-222222222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222222222000000002222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ39222222222222222-2-2-2-2-2-2222-2-2-2-2222222-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222i2i−2i−2i−2i−2i2i2i222i2i−2i−2i2222-2-2-2-200000000−2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ40222222222222222-2-2-2-2-2-2222-2-2-2-2222222-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222−2i−2i2i2i2i2i−2i−2i22−2i−2i2i2i2222-2-2-2-2000000002i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ4122222222222-2-2-2-22222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-20000000000000000222222222-2-2-2-2-2-20000000000000000-2-20000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ4222222222222-2-2-2-22222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-20000000000000000222222222-2-2-2-2-2-20000000000000000-2-200000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ4322222222222-2-2-2-22222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-200000000000000002-2-2-2-2-2-2-2-2-2-222220000000000000000220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000000000000000
χ4422222222222-2-2-2-22222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-200000000000000002-2-2-2-2-2-2-2-2-2-2222200000000000000002200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000000000000000
χ4522222222222-2-2-2-222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22-2-222-2-2-2-222220000000000000000-22i2i2i2i−2i−2i−2i−2i22−2i−2i2i2i0000000000000000−2i2i0000000022−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4622222222222-2-2-2-222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22-2-222-2-2-2-222220000000000000000-22i2i2i2i−2i−2i−2i−2i22−2i−2i2i2i0000000000000000−2i2i00000000−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4722222222222-2-2-2-222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22-2-222-2-2-2-222220000000000000000-2−2i−2i−2i−2i2i2i2i2i222i2i−2i−2i00000000000000002i−2i0000000022−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ4822222222222-2-2-2-222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22-2-222-2-2-2-222220000000000000000-2−2i−2i−2i−2i2i2i2i2i222i2i−2i−2i00000000000000002i−2i00000000−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ4922222222222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-222-2-222-2-222-2-2-2-20000000000000000220000000022−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222000000000000000000000000
χ5022222222222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-222-2-222-2-222-2-2-2-200000000000000002200000000−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2000000000000000000000000
χ5122222222222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-222-2-2222222220000000000000000-2-20000000022−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−2000000000000000000000000
χ5222222222222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-222-2-2222222220000000000000000-2-200000000−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−222000000000000000000000000
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χ13788888-8-8-8-8004242−42−42880000000000042−4242−4242−42-800004242−42−42000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ15316-16000000082−828ζ−8ζ7−8ζ+8ζ78ζ3−8ζ5−8ζ3+8ζ58-80000000000000000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ15516-16000000082−82−8ζ+8ζ78ζ−8ζ7−8ζ3+8ζ58ζ3−8ζ58-80000000000000000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ15616-16000000082−82−8ζ+8ζ78ζ−8ζ7−8ζ3+8ζ58ζ3−8ζ5-8800000000000000000000−42424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ15716-160000000−82828ζ3−8ζ5−8ζ3+8ζ5−8ζ+8ζ78ζ−8ζ78-800000000000000000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ15816-160000000−82828ζ3−8ζ5−8ζ3+8ζ5−8ζ+8ζ78ζ−8ζ7-880000000000000000000042−42−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ15916-160000000−8282−8ζ3+8ζ58ζ3−8ζ58ζ−8ζ7−8ζ+8ζ78-800000000000000000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ16016-160000000−8282−8ζ3+8ζ58ζ3−8ζ58ζ−8ζ7−8ζ+8ζ7-880000000000000000000042−424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.