Finite Group Databasebeta

← Group #72317554

Character table — Group #72317554

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size1111111122222222222244444444444444444444444488888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232
order12448888222444888888222222444444888888888888222244448888888822224444444444444444444488888888888888888888888844444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-11111
χ91111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1111-1-1-1-1-111-1-1iiii−i−i−i−i111111-1-1-1-1-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−i
χ101111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1111-1-1-1-1-111-1-1−i−i−i−iiiii111111-1-1-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii
χ111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1111-11-1-1-1-1-1-111iiii−i−i−i−i1111-1-111-1-1-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iii−i−iii-1-111ii−i−i−i−iii−i−iii
χ121111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1111-11-1-1-1-1-1-111−i−i−i−iiiii1111-1-111-1-1-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−iii−i−i-1-111−i−iiiii−i−iii−i−i
χ131111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11-1-1-11-1111111-1-1iiii−i−i−i−i-1-1-1-111-1-1111111-1-1iiii−i−i−i−i-1-111−i−iii−i−iiiii−i−i-1-111−i−iii−i−iiiii−i−i
χ141111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11-1-1-11-1111111-1-1−i−i−i−iiiii-1-1-1-111-1-1111111-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i−i−iii-1-111ii−i−iii−i−i−i−iii
χ151111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-1-111111-1-111iiii−i−i−i−i-1-1-1-1-1-1111111-1-111iiii−i−i−i−i11-1-1−i−iiiii−i−i−i−iii11-1-1−i−iiiii−i−i−i−iii
χ161111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-1-111111-1-111−i−i−i−iiiii-1-1-1-1-1-1111111-1-111−i−i−i−iiiii11-1-1ii−i−i−i−iiiii−i−i11-1-1ii−i−i−i−iiiii−i−i
χ171111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ181111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ191111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ201111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ211111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ221111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ231111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ241111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ251111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1111-1-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1111111-1-111−i−i−i−iiiii-1-111ii−i−i−i−iiiii−i−i11-1-1−i−iiiii−i−i−i−iii
χ261111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1111-1-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1111111-1-111iiii−i−i−i−i-1-111−i−iiiii−i−i−i−iii11-1-1ii−i−i−i−iiiii−i−i
χ271111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1111-11-1-1-1-1-1-111iiii−i−i−i−i-1-1-1-111-1-1111111-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i−i−iii-1-111−i−iii−i−iiiii−i−i
χ281111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1111-11-1-1-1-1-1-111−i−i−i−iiiii-1-1-1-111-1-1111111-1-1iiii−i−i−i−i11-1-1−i−iii−i−iiiii−i−i-1-111ii−i−iii−i−i−i−iii
χ291111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11-1-1-11-1111111-1-1iiii−i−i−i−i1111-1-111-1-1-1-1-1-111−i−i−i−iiiii11-1-1−i−iiiii−i−iii−i−i-1-111ii−i−i−i−iii−i−iii
χ301111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11-1-1-11-1111111-1-1−i−i−i−iiiii1111-1-111-1-1-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i−i−iii−i−iii-1-111−i−iiiii−i−iii−i−i
χ311111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-11-1-1-111111-1-111iiii−i−i−i−i111111-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-111−i−iii−i−iii−i−iii11-1-1ii−i−iii−i−iii−i−i
χ321111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-11-1-1-111111-1-111−i−i−i−iiiii111111-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-111ii−i−iii−i−iii−i−i11-1-1−i−iii−i−iii−i−iii
χ33222222222222222222222222-2-22222-2-222222222-2-2-2-2-2-2-22-2-2-22-2-2-2-222-2-2002-2002-20000-2-22200000000000022-2-20000-2-2220000000000000000000000000000000000000000
χ34222222222222222222222222-2-22222-2-222222222-2-2-2-2-2-2-22-2-2-22-2-2-2-222-2-200-2200-22000022-2-2000000000000-2-222000022-2-20000000000000000000000000000000000000000
χ352222222222222222222222-2-22222-2-2222222-2-2-2-22222-2-22-2-2-22-2-2-2-2-2-2-222002200220000-2-2-2-200000000000022220000-2-2-2-20000000000000000000000000000000000000000
χ362222222222222222222222-2-22222-2-2222222-2-2-2-22222-2-22-2-2-22-2-2-2-2-2-2-22200-2-200-2-200002222000000000000-2-2-2-2000022220000000000000000000000000000000000000000
χ3722222222222222222222-2-22222-2-22222-2-2-2-2222222222-2-2-22-2-2-222-2-2-2-2-2-200000000000000000000000000000000000000000000000000002-22-20000000000002-22-200000000
χ3822222222222222222222-2-22222-2-22222-2-2-2-2222222222-2-2-22-2-2-222-2-2-2-2-2-20000000000000000000000000000000000000000000000000000-22-22000000000000-22-2200000000
χ3922222222222222222222-2-222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-222-2-222-2-2-222-2-222000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i0000
χ4022222222222222222222-2-222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-222-2-222-2-2-222-2-22200000000000000000000000000000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i0000
χ4122222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222-22-22-22-22-2-22222-2-2000000000000000000000000000000000000000000000000000000002-2-220000000000002-2-220000
χ4222222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222-22-22-22-22-2-22222-2-200000000000000000000000000000000000000000000000000000000-222-2000000000000-222-20000
χ4322222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2222-22222-2-2222200000000000000000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i00000000
χ4422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2222-22222-2-222220000000000000000000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i00000000
χ452222-2-2-2-2222222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-22-2-2-222222-2-222002-2002-20000-2-222000000000000-2-222000022-2-20000000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-22-2-2-222222-2-22200-2200-22000022-2-200000000000022-2-20000-2-2220000000000000000000000000000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-222-2-22222-2-222-2-2-2-22222-2-2-2-2-2-22-2-2-22-2222222-2-2002200220000-2-2-2-2000000000000-2-2-2-2000022220000000000000000000000000000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-222-2-22222-2-222-2-2-2-22222-2-2-2-2-2-22-2-2-22-2222222-2-200-2-200-2-20000222200000000000022220000-2-2-2-20000000000000000000000000000000000000000
χ492222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-22-2-2-22-2-2-2-2-222222200000000000000000000000000000000000000000000000000002-22-2000000000000-22-2200000000
χ502222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-22-2-2-22-2-2-2-2-22222220000000000000000000000000000000000000000000000000000-22-220000000000002-22-200000000
χ512222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222-222-2-222-222-2-222-2-2000000000000000000000000000000000000000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i0000
χ522222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-22222-222-2-222-222-2-222-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000
χ532222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2-22-22-22-2222-2-2-2-222000000000000000000000000000000000000000000000000000000002-2-22000000000000-222-20000
χ542222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2-22-22-22-2222-2-2-2-22200000000000000000000000000000000000000000000000000000000-222-20000000000002-2-220000
χ552222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222-2222-222-2-222-2-2-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i000000000000−2i2i2i−2i00000000
χ562222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222-2222-222-2-222-2-2-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i0000000000002i−2i−2i2i00000000
χ5722-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i222222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-2-22-222-22i−2i2i−2i2i−2i2i−2i000000000000000022-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ5822-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i222222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-2-22-222-22i−2i2i−2i2i−2i2i−2i0000000000000000-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ5922-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i2222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22222-2-2-2−2i2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000000000002-22-20000000000002i−2i2i−2i
χ6022-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i2222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22222-2-2-2−2i2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000000000000000-22-22000000000000−2i2i−2i2i
χ6122-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i22-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-2-22-222−2i2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000002i−2i−2i2i000000000000-222-2
χ6222-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i22-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-2-22-222−2i2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000000000002-2-22
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.