Finite Group Databasebeta

← Group #72227267

Character table — Group #72227267

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124
size112222222222244444444888888888888888888888888888888888888816161616161616161616323232323232323232323232323232326464646464646464646464646464646464646464646464646464646464646464128128128128128128128128
order12222444488884488888844444888888888888161616161616161616161616161616161616161688881616161616163232323232323232323232323232323288881616161632323232323232323232323232323232323232323232323224888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-1ii−i−i
χ101111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-111−i−iii
χ111111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-111−i−iii
χ121111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1ii−i−i
χ131111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1−i−iii
χ141111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-111ii−i−i
χ151111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-111ii−i−i
χ161111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−i−iii
χ17111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−i11-1-1ii−i−i1-1i−iζ−ζζ3−ζ3
χ18111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i-1-111−i−iii-11−ii−ζζ−ζ3ζ3
χ19111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii11-1-1ii−i−i-11−ii−ζζ−ζ3ζ3
χ20111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iii-1-111−i−iii1-1i−iζ−ζζ3−ζ3
χ21111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-1-111−i−iii-1-111−i−iii1-1i−i−ζζ−ζ3ζ3
χ22111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-1-111−i−iii11-1-1ii−i−i-11−iiζ−ζζ3−ζ3
χ23111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ311-1-1ii−i−i-1-111−i−iii-11−iiζ−ζζ3−ζ3
χ24111-1-111-1-1-1-1-1-1111111-1-1-1i−ii−ii−i1111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ311-1-1ii−i−i11-1-1ii−i−i1-1i−i−ζζ−ζ3ζ3
χ25111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iii11-1-1−i−iii1-1−iiζ3−ζ3ζ−ζ
χ26111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii-1-111ii−i−i-11i−i−ζ3ζ3−ζζ
χ27111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i11-1-1−i−iii-11i−i−ζ3ζ3−ζζ
χ28111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−i-1-111ii−i−i1-1−iiζ3−ζ3ζ−ζ
χ29111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-1-111ii−i−i-1-111ii−i−i1-1−ii−ζ3ζ3−ζζ
χ30111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-1-111ii−i−i11-1-1−i−iii-11i−iζ3−ζ3ζ−ζ
χ31111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ11-1-1−i−iii-1-111ii−i−i-11i−iζ3−ζ3ζ−ζ
χ32111-1-111-1-1-1-1-1-1111111-1-1-1−ii−ii−ii1111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ11-1-1−i−iii11-1-1−i−iii1-1−ii−ζ3ζ3−ζζ
χ3322222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ3422222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ352222222222222222222222222222-2-2-2-2-2-2-2-2222-22-222222222-2-2-2-22-22-2-2-2-2-22-22-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ362222222222222222222222222222-2-2-2-2-2-2-2-2222-22-222222222-2-2-2-22-22-2-2-2-2-22-22-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ372222222222222222222222222222-2-2-2-2-2-2-2-222-22-22-2-2-2-2-2-2-2-22222-22-22-2-2-2-2-22-222200000000000000002222-2-2-2-200000000000000000000000000000000
χ382222222222222222222222222222-2-2-2-2-2-2-2-222-22-22-2-2-2-2-2-2-2-22222-22-22-2-2-2-2-22-22220000000000000000-2-2-2-2222200000000000000000000000000000000
χ392222222222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402222222222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-22-2-2-2-2-2-2-2-2-222222-22-222222-22-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ422222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-22-2-2-2-2-2-2-2-2-222222-22-222222-22-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ432222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2222222222-2-2-2-2-22-222222-22-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ442222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2222222222-2-2-2-2-22-222222-22-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4522222222222-2-2-2-222-2-22-2-222-2-2-2-20000000022-20-202222-2-2-2-20000-20-200000202000002i−2i002i−2i002i−2i002i−2i000000002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ4622222222222-2-2-2-222-2-22-2-222-2-2-2-20000000022-20-202222-2-2-2-20000-20-200000202000002i−2i002i−2i002i−2i002i−2i00000000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ4722222222222-2-2-2-222-2-22-2-222-2-2-2-20000000022-20-202222-2-2-2-20000-20-20000020200000−2i2i00−2i2i00−2i2i00−2i2i000000002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ4822222222222-2-2-2-222-2-22-2-222-2-2-2-20000000022-20-202222-2-2-2-20000-20-20000020200000−2i2i00−2i2i00−2i2i00−2i2i00000000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ4922222222222-2-2-2-222-2-22-2-2-2-2222200000000-2-2-20-20-2-2-2-222220000-20-200000202000002-2002-200-2200-2200000000i2−i2i2−i2−i2i2−i2i200000000−i2i2−i2i2i2−i2i2−i200000000
χ5022222222222-2-2-2-222-2-22-2-2-2-2222200000000-2-2-20-20-2-2-2-222220000-20-200000202000002-2002-200-2200-2200000000−i2i2−i2i2i2−i2i2−i200000000i2−i2i2−i2−i2i2−i2i200000000
χ5122222222222-2-2-2-222-2-22-2-2-2-2222200000000-2-2-20-20-2-2-2-222220000-20-20000020200000-2200-22002-2002-200000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i200000000
χ5222222222222-2-2-2-222-2-22-2-2-2-2222200000000-2-2-20-20-2-2-2-222220000-20-20000020200000-2200-22002-2002-200000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i200000000
χ53222-2-222-2-2-2-222-2-222-2-2-2222i−2i−2i2i−2i2i000000002i−2i-20202i2i−2i−2i−2i−2i2i2i0000-2020000020-2000002ζ3−2ζ300−2ζ32ζ300−2ζ2ζ002ζ−2ζ000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000i2−i2−i2i2−222−200000000
χ54222-2-222-2-2-2-222-2-222-2-2-2222i−2i−2i2i−2i2i000000002i−2i-20202i2i−2i−2i−2i−2i2i2i0000-2020000020-2000002ζ3−2ζ300−2ζ32ζ300−2ζ2ζ002ζ−2ζ00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000−i2i2i2−i22−2−2200000000
χ55222-2-222-2-2-2-222-2-222-2-2-2222i−2i−2i2i−2i2i000000002i−2i-20202i2i−2i−2i−2i−2i2i2i0000-2020000020-200000−2ζ32ζ3002ζ3−2ζ3002ζ−2ζ00−2ζ2ζ000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000−i2i2i2−i22−2−2200000000
χ56222-2-222-2-2-2-222-2-222-2-2-2222i−2i−2i2i−2i2i000000002i−2i-20202i2i−2i−2i−2i−2i2i2i0000-2020000020-200000−2ζ32ζ3002ζ3−2ζ3002ζ−2ζ00−2ζ2ζ00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000i2−i2−i2i2−222−200000000
χ57222-2-222-2-2-2-222-2-222-2-2-222−2i2i2i−2i2i−2i00000000−2i2i-2020−2i−2i2i2i2i2i−2i−2i0000-2020000020-2000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ3000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000i2−i2−i2i22−2−2200000000
χ58222-2-222-2-2-2-222-2-222-2-2-222−2i2i2i−2i2i−2i00000000−2i2i-2020−2i−2i2i2i2i2i−2i−2i0000-2020000020-2000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ300000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000−i2i2i2−i2−222−200000000
χ59222-2-222-2-2-2-222-2-222-2-2-222−2i2i2i−2i2i−2i00000000−2i2i-2020−2i−2i2i2i2i2i−2i−2i0000-2020000020-200000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ3000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000−i2i2i2−i2−222−200000000
χ60222-2-222-2-2-2-222-2-222-2-2-222−2i2i2i−2i2i−2i00000000−2i2i-2020−2i−2i2i2i2i2i−2i−2i0000-2020000020-200000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ300000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000i2−i2−i2i22−2−2200000000
χ61222-2-222-2-2-2-2-2-2222222-2-2-22i−2i2i−2i2i−2i2222-2-2-2-22i−2i-2-222−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i-2-222−2i2i000000000000000000000000000000002i−2i−2i2i-222-20000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.