Finite Group Databasebeta

← Group #72312753

Character table — Group #72312753

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size111122222244444444444444444444444488888888888888888888888888888888881616161616161616161616161616161616161616161616163232323232323232
order1222224444222222444444444444444444222222444444444444444444448888888822224444444488888888888844448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-11111-1-111111111-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-111111111-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-111111111-1-111-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111111111111-1-111-1-1
χ91111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ171-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i11-1-1111-11-111-1-1ii−i−i1-111-1-1ii−i−iii−i−i1-1ii−i−iii−i−i1-11-1i−ii−i1-11-1i−ii−i11-1-1ii−i−ii−ii−i1-11-1
χ181-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i11-1-1111-11-111-1-1ii−i−i1-111-1-1ii−i−iii−i−i1-1−i−iii−i−iii-11-11i−ii−i-11-11−ii−ii11-1-1ii−i−i−ii−ii-11-11
χ191-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i11-1-1111-11-1-1-111−i−iii1-1-1-111ii−i−i−i−iii1-1ii−i−iii−i−i1-11-1i−ii−i1-11-1i−ii−i-1-111−i−iii−ii−ii-11-11
χ201-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i11-1-1111-11-1-1-111−i−iii1-1-1-111ii−i−i−i−iii1-1−i−iii−i−iii-11-11i−ii−i-11-11−ii−ii-1-111−i−iiii−ii−i1-11-1
χ211-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i-1-111111-1-1111-1-1ii−i−i-1111-1-1ii−i−iii−i−i-11ii−i−i−i−iii1-1-11−ii−ii1-1-11i−i−ii-1-111−i−iiii−i−ii1-1-11
χ221-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i-1-111111-1-1111-1-1ii−i−i-1111-1-1ii−i−iii−i−i-11−i−iiiii−i−i-111-1−ii−ii-111-1−iii−i-1-111−i−iii−iii−i-111-1
χ231-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i-1-111111-1-11-1-111−i−iii-11-1-111ii−i−i−i−iii-11ii−i−i−i−iii1-1-11−ii−ii1-1-11i−i−ii11-1-1ii−i−i−iii−i-111-1
χ241-11-1-1111-1-1111-1-1-1ii−i−i-1-1ii−i−i-1-111111-1-11-1-111−i−iii-11-1-111ii−i−i−i−iii-11−i−iiiii−i−i-111-1−ii−ii-111-1−iii−i11-1-1ii−i−ii−i−ii1-1-11
χ251-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii11-1-1111-11-111-1-1−i−iii1-111-1-1−i−iii−i−iii1-1ii−i−iii−i−i-11-11−ii−ii-11-11i−ii−i11-1-1−i−iiii−ii−i-11-11
χ261-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii11-1-1111-11-111-1-1−i−iii1-111-1-1−i−iii−i−iii1-1−i−iii−i−iii1-11-1−ii−ii1-11-1−ii−ii11-1-1−i−iii−ii−ii1-11-1
χ271-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii11-1-1111-11-1-1-111ii−i−i1-1-1-111−i−iiiii−i−i1-1ii−i−iii−i−i-11-11−ii−ii-11-11i−ii−i-1-111ii−i−i−ii−ii1-11-1
χ281-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii11-1-1111-11-1-1-111ii−i−i1-1-1-111−i−iiiii−i−i1-1−i−iii−i−iii1-11-1−ii−ii1-11-1−ii−ii-1-111ii−i−ii−ii−i-11-11
χ291-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii-1-111111-1-1111-1-1−i−iii-1111-1-1−i−iii−i−iii-11ii−i−i−i−iii-111-1i−ii−i-111-1i−i−ii-1-111ii−i−ii−i−ii-111-1
χ301-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii-1-111111-1-1111-1-1−i−iii-1111-1-1−i−iii−i−iii-11−i−iiiii−i−i1-1-11i−ii−i1-1-11−iii−i-1-111ii−i−i−iii−i1-1-11
χ311-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii-1-111111-1-11-1-111ii−i−i-11-1-111−i−iiiii−i−i-11ii−i−i−i−iii-111-1i−ii−i-111-1i−i−ii11-1-1−i−iii−iii−i1-1-11
χ321-11-1-1111-1-1111-1-1-1−i−iii-1-1−i−iii-1-111111-1-11-1-111ii−i−i-11-1-111−i−iiiii−i−i-11−i−iiiii−i−i1-1-11i−ii−i1-1-11−iii−i11-1-1−i−iiii−i−ii-111-1
χ3322222222222-2-22-2-22222-2-2222222222-2-22-2-200000000-2-20000-2-2-2-2000022000000000000-2-222000000000000000000000000
χ3422222222222-2-22-2-22222-2-22222-2-2-2-22-2-222200000000220000-2-2-2-20000-2-200000000000022-2-2000000000000000000000000
χ3522222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222222-2-22-2-200000000-2-20000222200002200000000000022-2-2000000000000000000000000
χ3622222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-22220000000022000022220000-2-2000000000000-2-222000000000000000000000000
χ372222222222-22-2-22-222222-2-2-2-2-20000-22-2-200000000000000002-22-20000000000222200-2-20000002200-2-20000000000000000
χ382222222222-22-2-22-222222-2-2-2-2-20000-22-2-200000000000000002-22-20000000000-2-2-2-20022000000-2-200220000000000000000
χ392222222222-22-2-22-2-2-2-2-22-222220000-22-2-20000000000000000-22-22000000000022220022000000-2-200-2-20000000000000000
χ402222222222-22-2-22-2-2-2-2-22-222220000-22-2-20000000000000000-22-220000000000-2-2-2-200-2-20000002200220000000000000000
χ412222222222-2-22-2-222222-22-2-2-2-20000-2-22-20000000000000000-22-2200000022220000-2-20000002200-2-2000000000000000000
χ422222222222-2-22-2-222222-22-2-2-2-20000-2-22-20000000000000000-22-22000000-2-2-2-2000022000000-2-20022000000000000000000
χ432222222222-2-22-2-22-2-2-2-2-2222220000-2-22-200000000000000002-22-20000002222000022000000-2-200-2-2000000000000000000
χ442222222222-2-22-2-22-2-2-2-2-2222220000-2-22-200000000000000002-22-2000000-2-2-2-20000-2-2000000220022000000000000000000
χ45222222-2-2-2-2-222-2220000-2-2000022222-2-222200002-22-2-2-2000000002-22-2-2-200000000000000000000000000002-22-200000000
χ46222222-2-2-2-2-222-2220000-2-2000022222-2-22220000-22-22-2-200000000-22-22-2-20000000000000000000000000000-22-2200000000
χ47222222-2-2-2-2-222-2220000-2-20000-2-2-2-22-2-22-2-200002-22-222000000002-22-2220000000000000000000000000000-22-2200000000
χ48222222-2-2-2-2-222-2220000-2-20000-2-2-2-22-2-22-2-20000-22-222200000000-22-222200000000000000000000000000002-22-200000000
χ49222222-2-2-2-2-2-2-2-2-2-2000022000022222222-2-22-22-20000222-22-200000000-2-20000000000000000000000002-22-2000000000000
χ50222222-2-2-2-2-2-2-2-2-2-2000022000022222222-2-2-22-22000022-22-2200000000-2-2000000000000000000000000-22-22000000000000
χ51222222-2-2-2-2-2-2-2-2-2-20000220000-2-2-2-22222222-22-20000-2-22-22-20000000022000000000000000000000000-22-22000000000000
χ52222222-2-2-2-2-2-2-2-2-2-20000220000-2-2-2-2222222-22-220000-2-2-22-2200000000220000000000000000000000002-22-2000000000000
χ532-22-2-2222-2-22-2-2-2222i2i−2i−2i222i2i−2i−2i22-2-22-2-2-2-2200000000-220000−2i−2i2i2i00002-2000000000000−2i2i2i−2i000000000000000000000000
χ542-22-2-2222-2-22-2-2-2222i2i−2i−2i222i2i−2i−2i-2-2222-2-2-22-2000000002-20000−2i−2i2i2i0000-220000000000002i−2i−2i2i000000000000000000000000
χ552-22-2-2222-2-22-2-2-222−2i−2i2i2i22−2i−2i2i2i22-2-22-2-2-2-2200000000-2200002i2i−2i−2i00002-20000000000002i−2i−2i2i000000000000000000000000
χ562-22-2-2222-2-22-2-2-222−2i−2i2i2i22−2i−2i2i2i-2-2222-2-2-22-2000000002-200002i2i−2i−2i0000-22000000000000−2i2i2i−2i000000000000000000000000
χ572-22-2-2222-2-2-22-22-222i2i−2i−2i-22−2i−2i2i2i0000-22-2200000000000000002i−2i−2i2i00000000002i2i−2i−2i00-220000002-200−2i2i0000000000000000
χ582-22-2-2222-2-2-22-22-222i2i−2i−2i-22−2i−2i2i2i0000-22-2200000000000000002i−2i−2i2i0000000000−2i−2i2i2i002-2000000-22002i−2i0000000000000000
χ592-22-2-2222-2-2-22-22-22−2i−2i2i2i-222i2i−2i−2i0000-22-220000000000000000−2i2i2i−2i00000000002i2i−2i−2i002-2000000-2200−2i2i0000000000000000
χ602-22-2-2222-2-2-22-22-22−2i−2i2i2i-222i2i−2i−2i0000-22-220000000000000000−2i2i2i−2i0000000000−2i−2i2i2i00-220000002-2002i−2i0000000000000000
χ612-22-2-2222-2-2-2-2222-22i2i−2i−2i2-2−2i−2i2i2i0000-2-2220000000000000000−2i2i2i−2i0000002i2i−2i−2i0000-220000002-200−2i2i000000000000000000
χ622-22-2-2222-2-2-2-2222-22i2i−2i−2i2-2−2i−2i2i2i0000-2-2220000000000000000−2i2i2i−2i000000−2i−2i2i2i00002-2000000-22002i−2i000000000000000000
χ632-22-2-2222-2-2-2-2222-2−2i−2i2i2i2-22i2i−2i−2i0000-2-22200000000000000002i−2i−2i2i0000002i2i−2i−2i00002-2000000-2200−2i2i000000000000000000
χ642-22-2-2222-2-2-2-2222-2−2i−2i2i2i2-22i2i−2i−2i0000-2-22200000000000000002i−2i−2i2i000000−2i−2i2i2i0000-220000002-2002i−2i000000000000000000
χ652-22-2-22-2-222-2222-2-2000022000022-2-22-2-2-22-200002i−2i−2i2i-22000000002i−2i−2i2i-2200000000000000000000000000002i−2i−2i2i00000000
χ662-22-2-22-2-222-2222-2-2000022000022-2-22-2-2-22-20000−2i2i2i−2i-2200000000−2i2i2i−2i-220000000000000000000000000000−2i2i2i−2i00000000
χ672-22-2-22-2-222-2222-2-20000220000-2-2222-2-2-2-2200002i−2i−2i2i2-2000000002i−2i−2i2i2-20000000000000000000000000000−2i2i2i−2i00000000
χ682-22-2-22-2-222-2222-2-20000220000-2-2222-2-2-2-220000−2i2i2i−2i2-200000000−2i2i2i−2i2-200000000000000000000000000002i−2i−2i2i00000000
χ692-22-2-22-2-222-2-2-22220000-2-2000022-2-2222-2-222-2-2200002-22-2-2200000000-220000000000000000000000002-2-22000000000000
χ702-22-2-22-2-222-2-2-22220000-2-2000022-2-2222-2-22-222-200002-2-222-200000000-22000000000000000000000000-222-2000000000000
χ712-22-2-22-2-222-2-2-22220000-2-20000-2-222222-22-22-2-220000-222-2-22000000002-2000000000000000000000000-222-2000000000000
χ722-22-2-22-2-222-2-2-22220000-2-20000-2-222222-22-2-222-20000-22-222-2000000002-20000000000000000000000002-2-22000000000000
χ73444444-4-4-4-444-444-40000-4400000000-4-44-4000000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-44-444-4400004-400000000-44-4-4000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-44-44-40000000000004-44-4000000000022222-22-200-2-2-2-20000-22-22000000000000000000000000000000000000000000
χ764444-4-44-44-40000000000004-44-40000000000-2-2-2-2-22-2200222200002-22-2000000000000000000000000000000000000000000
χ774444-4-44-44-4000000000000-44-4400000000002222-22-2200-2-2-2-200002-22-2000000000000000000000000000000000000000000
χ784444-4-44-44-4000000000000-44-440000000000-2-2-2-22-22-20022220000-22-22000000000000000000000000000000000000000000
χ794444-4-4-44-440000004-44-400000000000000002-22-2222200-22-220000-2-2-2-2000000000000000000000000000000000000000000
χ804444-4-4-44-440000004-44-40000000000000000-22-22-2-2-2-2002-22-200002222000000000000000000000000000000000000000000
χ814444-4-4-44-44000000-44-4400000000000000002-22-2-2-2-2-200-22-2200002222000000000000000000000000000000000000000000
χ824444-4-4-44-44000000-44-440000000000000000-22-222222002-22-20000-2-2-2-2000000000000000000000000000000000000000000
χ834-44-44-44-4-440000000000004i−4i−4i4i000000000022-2-22i−2i−2i2i00-2-2220000−2i2i2i−2i000000000000000000000000000000000000000000
χ844-44-44-44-4-440000000000004i−4i−4i4i0000000000-2-222−2i2i2i−2i0022-2-200002i−2i−2i2i000000000000000000000000000000000000000000
χ854-44-44-44-4-44000000000000−4i4i4i−4i000000000022-2-2−2i2i2i−2i00-2-22200002i−2i−2i2i000000000000000000000000000000000000000000
χ864-44-44-44-4-44000000000000−4i4i4i−4i0000000000-2-2222i−2i−2i2i0022-2-20000−2i2i2i−2i000000000000000000000000000000000000000000
χ874-44-44-4-444-40000004i−4i−4i4i00000000000000002-2-222i2i−2i−2i00-222-20000−2i−2i2i2i000000000000000000000000000000000000000000
χ884-44-44-4-444-40000004i−4i−4i4i0000000000000000-222-2−2i−2i2i2i002-2-2200002i2i−2i−2i000000000000000000000000000000000000000000
χ894-44-44-4-444-4000000−4i4i4i−4i00000000000000002-2-22−2i−2i2i2i00-222-200002i2i−2i−2i000000000000000000000000000000000000000000
χ904-44-44-4-444-4000000−4i4i4i−4i0000000000000000-222-22i2i−2i−2i002-2-220000−2i−2i2i2i000000000000000000000000000000000000000000
χ914-44-4-44-4-44444-4-4-4400004-400000000-4-444000000000000000000000000000000000000000000000000000000000000000000
χ924-44-4-44-4-4444-44-44-40000-4400000000-44-44000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-800000000000000000000004-44-40000000000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ9488-8-800000000000000000000004-44-4000000000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ9588-8-80000000000000000000000-44-440000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ9688-8-80000000000000000000000-44-44000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ978-8-8800000000000000000000004-4-4400000000000000000000000000000022−22−222222−22−222200000000000000000000000000000000
χ988-8-8800000000000000000000004-4-44000000000000000000000000000000−222222−22−222222−2200000000000000000000000000000000
χ998-8-880000000000000000000000-444-400000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ1008-8-880000000000000000000000-444-4000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).