Finite Group Databasebeta

← Group #72225358

Character table — Group #72225358

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size111122222222222222444444444444444444444444444444444444444444448888888888888888888888888888888888888832323232323232323232323232323232323232323232323232323232323232326464646464646464
order12442224448888888844444444888888888888888888888888888816161616161616164488888888161616161616161616161616161616161616161616161616161616168888888816161616161616163232323232323232323232323232323222448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-1
χ91111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111
χ111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111
χ121111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111
χ141111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111
χ1711-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1i−ii−i
χ1811-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−ii−ii
χ1911-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−ii−ii
χ2011-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1i−ii−i
χ2111-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−ii−i−i−i−i−iiiii11-1-1-1-111−i−iii11-1-1ii−i−i-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1-11i−i−ii
χ2211-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−ii−i−i−i−i−iiiii11-1-1-1-111−i−iii11-1-1ii−i−i-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-111-1−iii−i
χ2311-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−ii−i−i−i−i−iiiii11-1-1-1-111−i−iii11-1-1ii−i−i-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-111-1−iii−i
χ2411-1-11-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-11111111111-1-1ii−i−iiiii−i−i−i−ii−i−i−i−i−iiiii11-1-1-1-111−i−iii11-1-1ii−i−i-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1-11i−i−ii
χ2511-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−ii−ii
χ2611-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111i−ii−i
χ2711-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111i−ii−i
χ2811-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-111-1-1−i−iii11-1-1−i−iii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−ii−ii
χ2911-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiii−iiiiii−i−i−i−i11-1-1-1-111ii−i−i11-1-1−i−iii-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1-11−iii−i
χ3011-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiii−iiiiii−i−i−i−i11-1-1-1-111ii−i−i11-1-1−i−iii-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-111-1i−i−ii
χ3111-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiii−iiiiii−i−i−i−i11-1-1-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-111-1i−i−ii
χ3211-1-11-1-111-11111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−i−i−iiiii−iiiiii−i−i−i−i11-1-1-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1-11−iii−i
χ33222222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ352222222222222222222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ362222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ37222222222222-2-222-2-2-2-2-2-22222222200000000000000002-22-2-2-2-2-222222222-2-200000000-2-2-2-2000000002222-2-2-2-2000000002-22-22-22-200000000000000000000000000000000
χ38222222222222-2-222-2-2-2-2-2-22222222200000000000000002-22-2-2-2-2-222222222-2-200000000-2-2-2-2000000002222-2-2-2-200000000-22-22-22-2200000000000000000000000000000000
χ39222222222222-2-222-2-2-2-2-2-22222222200000000000000002-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-2222200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ40222222222222-2-222-2-2-2-2-2-22222222200000000000000002-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-2-2-2-222220000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ41222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002-22-22222222222222200000000222200000000-2-2-2-2-2-2-2-200000000000000002-22-2-22-22000000000000000000000000
χ42222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002-22-22222222222222200000000222200000000-2-2-2-2-2-2-2-20000000000000000-22-222-22-2000000000000000000000000
χ43222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002-22-22222-2-2-2-2-2-2-2-22200000000-2-2-2-20000000022222222000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ44222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002-22-22222-2-2-2-2-2-2-2-22200000000-2-2-2-2000000002222222200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ452222222222-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000-22-22222200000000-2-20000000000002222222200000000-2-2-2-2-2-2-2-200000000000000002−22−22−22−22−22−22−22−200000000
χ462222222222-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000-22-22222200000000-2-20000000000002222222200000000-2-2-2-2-2-2-2-20000000000000000−22−22−22−22−22−22−22−2200000000
χ472222222222-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000-22-22222200000000-2-2000000000000-2-2-2-2-2-2-2-2000000002222222200000000000000002−22−22−22−2−22−22−22−2200000000
χ482222222222-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000-22-22222200000000-2-2000000000000-2-2-2-2-2-2-2-200000000222222220000000000000000−22−22−22−222−22−22−22−200000000
χ492222222222-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000-22-22-2-2-2-200000000220000000000002222-2-2-2-200000000-2-2-2-222220000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ502222222222-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000-22-22-2-2-2-200000000220000000000002222-2-2-2-200000000-2-2-2-222220000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ512222222222-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000-22-22-2-2-2-20000000022000000000000-2-2-2-22222000000002222-2-2-2-20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ522222222222-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000-22-22-2-2-2-20000000022000000000000-2-2-2-22222000000002222-2-2-2-20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ5322-2-22-2-222-22222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i22222222-2-2-2-2-2-2-2-222-2-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i−2i2i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ5422-2-22-2-222-22222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2-2-22222222222-2-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i−2i−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i-2-222−2i−2i2i2i22-2-22i2i−2i−2i0000000000000000000000000000000000000000
χ5522-2-22-2-222-22222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i22222222-2-2-2-2-2-2-2-222-2-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i−2i2i−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i0000000000000000000000000000000000000000
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χ1388-8−8i8i000000−424242−424i2−4i2−4i24i2-444i−4i00000000−4+224−224+22−4−22−222222−22−2ζ+4i−2ζ32ζ−4i+2ζ3−2ζ−4i−2ζ32ζ+4i+2ζ32i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1398-8−8i8i000000−4242−42424i2−4i24i2−4i24-4−4i4i0000000022−2222−22−4+224−22−4−224+22−2i22i2−2i22i2−2ζ+4i−2ζ32ζ−4i+2ζ3−2ζ−4i−2ζ32ζ+4i+2ζ30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1408-8−8i8i000000−4242−42424i2−4i24i2−4i24-4−4i4i00000000−2222−22224−22−4+224+22−4−222i2−2i22i2−2i22ζ−4i+2ζ3−2ζ+4i−2ζ32ζ+4i+2ζ3−2ζ−4i−2ζ30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.