Finite Group Databasebeta

← Group #72343221

Character table — Group #72343221

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111122222244444444444444444444888888888888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616163232323232323232646464646464646464646464
order12442488882224444444448888888822444444488888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616248816161616444888161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ511111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111
χ611111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-1-1-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111111-1-1-1-1-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1111111
χ91111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1-11-1-1-111-1-1
χ101111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-111
χ111111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-11-1-11-1-1-1-111
χ121111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-11111-1-1
χ131111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-111111-1-1
χ141111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-111-1-1-1-1-111
χ151111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-111-1-111
χ161111111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-11-1-111-1-1
χ17111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-1ii−i−i-1111-1-1i−ii−ii−i
χ18111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111−i−iii1-1-1-111−ii−ii−ii
χ19111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-1ii−i−i-1-1-1111i−i−ii−ii
χ20111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-111−i−iii111-1-1-1−iii−ii−i
χ21111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-1−i−iii-1-1-1111−iii−ii−i
χ22111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-111ii−i−i111-1-1-1i−i−ii−ii
χ23111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-1−i−iii-1111-1-1−ii−ii−ii
χ24111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111-1-111111-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111ii−i−i1-1-1-111i−ii−ii−i
χ25111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-1111111-1-1ii−i−i11-1-1-11−iii−i−ii
χ26111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-1-111−i−iii-1-1111-1i−i−iii−i
χ27111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-111-1-1ii−i−i1-11-11-1−ii−iii−i
χ28111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-1-111−i−iii-11-11-11i−ii−i−ii
χ29111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-111-1-1−i−iii1-11-11-1i−ii−i−ii
χ30111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1-1-111ii−i−i-11-11-11−ii−iii−i
χ31111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-1111111-1-1−i−iii11-1-1-11i−i−iii−i
χ32111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-111-1-111111-1-111−i−i−i−iiiii−i−iiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-1-111ii−i−i-1-1111-1−iii−i−ii
χ3322222222222222222222-2-2222222-2-22-22-2-2-2-2-2-2-2-222-2-2-2-2-222000000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ3422222222222222222222-2-2222222-2-22-22-2-2-2-2-2-2-2-222-2-2-2-2-22200000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ352222222222222-2-2-2-2222-2-2222222-2-2-22-22-2-2-22222-2-2-2-2-222-2-2000000000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000000000
χ362222222222222-2-2-2-2222-2-2222222-2-2-22-22-2-2-22222-2-2-2-2-222-2-200000000000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000000000
χ3722222222222-2-200002-2-22222-2-2-2-22200002-2-20000002-2-2000022-2-222-2-22-22-20000000000002-22-20000-22-220000000022-2-222-2-200000000000000000000
χ3822222222222-2-200002-2-22222-2-2-2-22200002-2-20000002-2-2000022-2-222-2-22-22-2000000000000-22-2200002-22-200000000-2-222-2-22200000000000000000000
χ3922222222222-2-200002-2-22222-2-2-2-22200002-2-20000002-2-20000-2-222-2-222-22-220000000000002-22-20000-22-2200000000-2-222-2-22200000000000000000000
χ4022222222222-2-200002-2-22222-2-2-2-22200002-2-20000002-2-20000-2-222-2-222-22-22000000000000-22-2200002-22-20000000022-2-222-2-200000000000000000000
χ4122222222222-2-200002-2-2-2-222-2-2-2-2-2-20000-222000000-22200000000000000002i2i−2i−2i2i2i−2i−2i000022220000-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ4222222222222-2-200002-2-2-2-222-2-2-2-2-2-20000-222000000-22200000000000000002i2i−2i−2i2i2i−2i−2i0000-2-2-2-200002222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ4322222222222-2-200002-2-2-2-222-2-2-2-2-2-20000-222000000-2220000000000000000−2i−2i2i2i−2i−2i2i2i000022220000-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ4422222222222-2-200002-2-2-2-222-2-2-2-2-2-20000-222000000-2220000000000000000−2i−2i2i2i−2i−2i2i2i0000-2-2-2-2000022222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ452222222222-22-20000-22-222-2-222-2-2220000-22-2000000-22-2000022-2-222-2-2-22-22000000002-22-20000-22-2200002-22-22-22-20000000000000000000000000000
χ462222222222-22-20000-22-222-2-222-2-2220000-22-2000000-22-2000022-2-222-2-2-22-2200000000-22-2200002-22-20000-22-22-22-220000000000000000000000000000
χ472222222222-22-20000-22-222-2-222-2-2220000-22-2000000-22-20000-2-222-2-2222-22-2000000002-22-20000-22-220000-22-22-22-220000000000000000000000000000
χ482222222222-22-20000-22-222-2-222-2-2220000-22-2000000-22-20000-2-222-2-2222-22-200000000-22-2200002-22-200002-22-22-22-20000000000000000000000000000
χ492222222222-22-20000-22-2-2-2-2-222-2-2-2-200002-220000002-2200000000000000002i−2i2i−2i2i−2i2i−2i22220000-2-2-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ502222222222-22-20000-22-2-2-2-2-222-2-2-2-200002-220000002-2200000000000000002i−2i2i−2i2i−2i2i−2i-2-2-2-200002222000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ512222222222-22-20000-22-2-2-2-2-222-2-2-2-200002-220000002-220000000000000000−2i2i−2i2i−2i2i−2i2i22220000-2-2-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ522222222222-22-20000-22-2-2-2-2-222-2-2-2-200002-220000002-220000000000000000−2i2i−2i2i−2i2i−2i2i-2-2-2-2000022220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ532222222222-2-222222-2-2222-2-2-2-22222-22-22-2-22-2-222-2-2-2-22-2-22222222222-2-2-2-22-2-222-2-220000000000000000000000000000000000000000000000000000
χ542222222222-2-222222-2-2222-2-2-2-22222-22-22-2-22-2-222-2-2-2-22-2-222-2-2-2-2-2-2-2-22222-222-2-222-20000000000000000000000000000000000000000000000000000
χ552222222222-2-222222-2-22-2-2-2-2-2-222-2-2-2-2-2-222-222-2-2-2-222-222220000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ562222222222-2-222222-2-22-2-2-2-2-2-222-2-2-2-2-2-222-222-2-2-2-222-22222000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ572222222222-2-22-2-2-2-2-2-2222-2-2-2-222222-22-2-2-2222-2-222-2-2222-2-222222222-2-2-2-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ582222222222-2-22-2-2-2-2-2-2222-2-2-2-222222-22-2-2-2222-2-222-2-2222-2-2-2-2-2-2-2-2-2-222222-2-222-2-220000000000000000000000000000000000000000000000000000
χ592222222222-2-22-2-2-2-2-2-22-2-2-2-2-2-222-2-2222222-2-2-2222222-2-2-2-2-20000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ602222222222-2-22-2-2-2-2-2-22-2-2-2-2-2-222-2-2222222-2-2-2222222-2-2-2-2-2000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ61222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ62222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-200000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ63222222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22222-2-2-22222000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ64222222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22222-2-2-2222200000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ65222222-2-2-2-22-2-200002-2-222-2-22222-2-200002-2-2000000-222000000000000000022-2-2-2-22200002i2i−2i−2i0000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ66222222-2-2-2-22-2-200002-2-222-2-22222-2-200002-2-2000000-222000000000000000022-2-2-2-2220000−2i−2i2i2i00002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ67222222-2-2-2-22-2-200002-2-222-2-22222-2-200002-2-2000000-2220000000000000000-2-22222-2-200002i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ68222222-2-2-2-22-2-200002-2-222-2-22222-2-200002-2-2000000-2220000000000000000-2-22222-2-20000−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ69222222-2-2-2-22-2-200002-2-2-2-2-2-22222220000-2220000002-2-200002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i0000000000002i−2i−2i2i0000−2i2i2i−2i0000000022-2-2-2-22200000000000000000000
χ70222222-2-2-2-22-2-200002-2-2-2-2-2-22222220000-2220000002-2-200002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i000000000000−2i2i2i−2i00002i−2i−2i2i00000000-2-22222-2-200000000000000000000
χ71222222-2-2-2-22-2-200002-2-2-2-2-2-22222220000-2220000002-2-20000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i0000000000002i−2i−2i2i0000−2i2i2i−2i00000000-2-22222-2-200000000000000000000
χ72222222-2-2-2-22-2-200002-2-2-2-2-2-22222220000-2220000002-2-20000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i000000000000−2i2i2i−2i00002i−2i−2i2i0000000022-2-2-2-22200000000000000000000
χ73222222-2-2-2-2-22-20000-22-22222-2-222-2-20000-22-20000002-2200000000000000002-22-2-22-222i2i−2i−2i0000−2i−2i2i2i000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
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χ10544-4-4-444i−4i−4i4i00000000004i−4i0000004-400000000000000000000004ζ3−4ζ3004ζ−4ζ000000000000000000000000000000000000000000002-22i−2i2ζ3−2ζ32ζ−2ζ000000000000
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χ10944-4-4-44−4i4i4i−4i0000000000−4i4i0000004-400000000000000000000004ζ−4ζ004ζ3−4ζ3000000000000000000000000000000000000000000002-2−2i2i2ζ−2ζ2ζ3−2ζ3000000000000
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χ1138888-8-888-8-800000000000000000000000000000000000000004i2−4i2004i2−4i2000000000000000000000000000000000000000000000000000000000000000000
χ1148888-8-888-8-80000000000000000000000000000000000000000−4i24i200−4i24i2000000000000000000000000000000000000000000000000000000000000000000
χ1158888-8-8-8-888000000000000000000000000000000000000000042−4200−4242000000000000000000000000000000000000000000000000000000000000000000
χ1168888-8-8-8-8880000000000000000000000000000000000000000−42420042−42000000000000000000000000000000000000000000000000000000000000000000
χ11788-8-8-888i−8i−8i8i0000000000−8i8i000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11888-8-8-88−8i8i8i−8i00000000008i−8i000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11916-1616i−16i0000000008-88i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12016-1616i−16i000000000-88−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12116-16−16i16i0000000008-8−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12216-16−16i16i000000000-888i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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