Finite Group Databasebeta

← Group #72321408

Character table — Group #72321408

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11112222222222222222224444444444888888888888888888888888888888888816161616161616161616161616161616161616161616161616163232323232323232
order1222222222444444448888444488888822444488888888888816161616161616161616161616161616224444444444448888161616161616161644888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ711111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ811111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ91111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ101111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ111111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ121111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ131111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ141111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ151111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ161111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111
χ171-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-1111-1i−i1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1i−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ181-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-1111-1i−i1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-1-111i−i−i−iii−i−iii11-1-111-1-1−ii−ii-11-11
χ191-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-1111-1i−i1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-1-111i−i−i−iiiii−i−i-1-111-1-111i−i−ii1-1-11
χ201-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-1111-1i−i1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiii-11-1111-1-1i−iii−i−i−i−iii-1-111-1-111−iii−i-111-1
χ211-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-111-11i−i-11ii−i−i-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-11-111-1-1−iiii−i−i−i−iii11-1-1-1-111i−i−ii-11-11
χ221-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-111-11i−i-11ii−i−i-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-11-1-111−ii−i−iiiii−i−i11-1-1-1-111−iii−i1-11-1
χ231-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-111-11i−i-11ii−i−i-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−ii−i−iii−i−iii-1-11111-1-1i−ii−i-111-1
χ241-1-1111-11-1-111-1-11-1-1111-1-1ii−i−i1-1-1-111-11i−i-11ii−i−i-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1−iiii−i−iii−i−i-1-11111-1-1−ii−ii1-1-11
χ251-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-1111-1−ii1-1−i−iii11-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-1-111−iiii−i−i−i−iii-1-111-1-111−iii−i1-1-11
χ261-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-1111-1−ii1-1−i−iii11-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i-11-1111-1-1−ii−i−iiiii−i−i-1-111-1-111i−i−ii-111-1
χ271-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-1111-1−ii1-1−i−iii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−ii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ281-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-1111-1−ii1-1−i−iii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111−iiii−i−iii−i−i11-1-111-1-1i−ii−i-11-11
χ291-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-111-11−ii-11−i−iii-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111i−iii−i−iii−i−i-1-11111-1-1−ii−ii-111-1
χ301-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-111-11−ii-11−i−iii-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1i−i−i−iii−i−iii-1-11111-1-1i−ii−i1-1-11
χ311-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-111-11−ii-11−i−iii-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-111-1-1i−i−i−iiiii−i−i11-1-1-1-111−iii−i-11-11
χ321-1-1111-11-1-111-1-11-1-1111-1-1−i−iii1-1-1-111-11−ii-11−i−iii-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-111i−iii−i−i−i−iii11-1-1-1-111i−i−ii1-11-1
χ33222222222222222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022000000000000000000000000
χ34222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-222222222000000000000000000000000-2-2000000000000000000000000
χ35222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222000000000000000000000000-2-2000000000000000000000000
χ36222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000022000000000000000000000000
χ372222222222-2-2-2-2-2-2-2-20000222200000000-2-20000002i−2i2i−2i2i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000002−22−2i2−i2i2−i200000000
χ382222222222-2-2-2-2-2-2-2-20000222200000000-2-20000002i−2i2i−2i2i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000−22−22−i2i2−i2i200000000
χ392222222222-2-2-2-2-2-2-2-20000222200000000-2-2000000−2i2i−2i2i−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000002−22−2−i2i2−i2i200000000
χ402222222222-2-2-2-2-2-2-2-20000222200000000-2-2000000−2i2i−2i2i−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000−22−22i2−i2i2−i200000000
χ412222222222-2-2-2-2-2-2-2-20000-2-2-2-200000000220000002i−2i2i−2i−2i2i−2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000−22−22−i2i2−i2i200000000
χ422222222222-2-2-2-2-2-2-2-20000-2-2-2-200000000220000002i−2i2i−2i−2i2i−2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000002−22−2i2−i2i2−i200000000
χ432222222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022000000−2i2i−2i2i2i−2i2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000−22−22i2−i2i2−i200000000
χ442222222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022000000−2i2i−2i2i2i−2i2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000002−22−2−i2i2−i2i200000000
χ4522222-22-2-2-22-2-2222-2-222220000-22-2-22-2000000000000000000000000002-22-22-22-200002i−2i2i−2i0000002i−2i2i−2i0000000000000000
χ4622222-22-2-2-22-2-2222-2-222220000-22-2-22-2000000000000000000000000002-22-22-22-20000−2i2i−2i2i000000−2i2i−2i2i0000000000000000
χ4722222-22-2-2-22-2-2222-2-222220000-22-2-22-200000000000000000000000000-22-22-22-2200002i−2i2i−2i000000−2i2i−2i2i0000000000000000
χ4822222-22-2-2-22-2-2222-2-222220000-22-2-22-200000000000000000000000000-22-22-22-220000−2i2i−2i2i0000002i−2i2i−2i0000000000000000
χ492222-22-2-22-2-2-2222-2-22-2-2-2-20000222-22-20000000000000000002i−2i2i−2i2i−2i2i−2i0000000022-2-20000002i−2i2i−2i00000000000000000000
χ502222-22-2-22-2-2-2222-2-22-2-2-2-20000222-22-20000000000000000002i−2i2i−2i2i−2i2i−2i00000000-2-222000000−2i2i−2i2i00000000000000000000
χ512222-22-2-22-2-2-2222-2-22-2-2-2-20000222-22-2000000000000000000−2i2i−2i2i−2i2i−2i2i0000000022-2-2000000−2i2i−2i2i00000000000000000000
χ522222-22-2-22-2-2-2222-2-22-2-2-2-20000222-22-2000000000000000000−2i2i−2i2i−2i2i−2i2i00000000-2-2220000002i−2i2i−2i00000000000000000000
χ532-2-2222-22-2-222-2-22-2-22-2-2222i2i−2i−2i-2222-2-22-22i−2i2-2−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000000000002i−2i000000000000000000000000
χ542-2-2222-22-2-222-2-22-2-22-2-2222i2i−2i−2i-2222-2-2-222i−2i-22−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000−2i2i000000000000000000000000
χ552-2-2222-22-2-222-2-22-2-22-2-222−2i−2i2i2i-2222-2-22-2−2i2i2-22i2i−2i−2i-2-2222i2i−2i−2i000000000000000000000000−2i2i000000000000000000000000
χ562-2-2222-22-2-222-2-22-2-22-2-222−2i−2i2i2i-2222-2-2-22−2i2i-222i2i−2i−2i22-2-2−2i−2i2i2i0000000000000000000000002i−2i000000000000000000000000
χ572-2-2222-22-2-2-2-222-222-200002i2i−2i−2i00000000−2i2i0000002i−2i−2i2i-222-2i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000002−2−22i2−i2−i2i200000000
χ582-2-2222-22-2-2-2-222-222-200002i2i−2i−2i00000000−2i2i0000002i−2i−2i2i-222-2−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000−222−2−i2i2i2−i200000000
χ592-2-2222-22-2-2-2-222-222-200002i2i−2i−2i00000000−2i2i000000−2i2i2i−2i2-2-22i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000002−2−22−i2i2i2−i200000000
χ602-2-2222-22-2-2-2-222-222-200002i2i−2i−2i00000000−2i2i000000−2i2i2i−2i2-2-22−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000−222−2i2−i2−i2i200000000
χ612-2-2222-22-2-2-2-222-222-20000−2i−2i2i2i000000002i−2i0000002i−2i−2i2i2-2-22i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000−222−2−i2i2i2−i200000000
χ622-2-2222-22-2-2-2-222-222-20000−2i−2i2i2i000000002i−2i0000002i−2i−2i2i2-2-22−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000002−2−22i2−i2−i2i200000000
χ632-2-2222-22-2-2-2-222-222-20000−2i−2i2i2i000000002i−2i000000−2i2i2i−2i-222-2i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000−222−2i2−i2−i2i200000000
χ642-2-2222-22-2-2-2-222-222-20000−2i−2i2i2i000000002i−2i000000−2i2i2i−2i-222-2−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000002−2−22−i2i2i2−i200000000
χ652-2-222-2-2-2222-22-22-22-222-2-20000-2-2222-2000000000000000000000000002i−2i2i−2i−2i2i−2i2i00002i−2i−2i2i000000-222-20000000000000000
χ662-2-222-2-2-2222-22-22-22-222-2-20000-2-2222-2000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000−2i2i2i−2i0000002-2-220000000000000000
χ672-2-222-2-2-2222-22-22-22-222-2-20000-2-2222-200000000000000000000000000−2i2i−2i2i2i−2i2i−2i00002i−2i−2i2i0000002-2-220000000000000000
χ682-2-222-2-2-2222-22-22-22-222-2-20000-2-2222-200000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000−2i2i2i−2i000000-222-20000000000000000
χ692-2-22-222-2-22-2-2-2-22222-2-22200002-2-222-20000000000000000002-22-2-22-22000000002-2-220000002-2-2200000000000000000000
χ702-2-22-222-2-22-2-2-2-22222-2-22200002-2-222-20000000000000000002-22-2-22-2200000000-222-2000000-222-200000000000000000000
χ712-2-22-222-2-22-2-2-2-22222-2-22200002-2-222-2000000000000000000-22-222-22-2000000002-2-22000000-222-200000000000000000000
χ722-2-22-222-2-22-2-2-2-22222-2-22200002-2-222-2000000000000000000-22-222-22-200000000-222-20000002-2-2200000000000000000000
χ7344444-44-4-4-44-4-4444-4-4-4-4-4-400004-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ7444444-44-4-4-4-444-4-4-44400000000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ7544444-44-4-4-4-444-4-4-4440000000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ764444-44-4-44-444-4-4-444-4000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ774444-44-4-44-444-4-4-444-400000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ784444-44-4-44-4-4-4444-4-4444440000-4-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ794444-4-4-44-444-44-4-44-44000000000000004400-4-400000000000000000000000000000000000000000000000000000000000000
χ804444-4-4-44-444-44-4-44-4400000000000000-4-4004400000000000000000000000000000000000000000000000000000000000000
χ814444-4-4-44-44-44-444-44-4444400004-44-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ824444-4-4-44-44-44-444-44-4-4-4-4-40000-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-4-4444-44-44-44-4-4-444000044-4-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-4-444-44-44-44-44000000000000000000000000000000000000000022−22−2222−222222−220000000000000000000000000000000000
χ854-4-444-4-4-444-44-44-44-440000000000000000000000000000000000000000−222222−2222−22−22220000000000000000000000000000000000
χ864-4-44-444-4-444444-4-4-4-40000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000000000000000
χ874-4-44-444-4-444444-4-4-4-400000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000
χ884-4-44-444-4-44-4-4-4-4444444-4-40000-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ894-4-44-4-4444-44-4-44-4-444000000000000004-400-4400000000000000000000000000000000000000000000000000000000000000
χ904-4-44-4-4444-44-4-44-4-44400000000000000-44004-400000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-4-444-444-4-444-4-4000044-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4444-4-444-444-4-4-4-4440000-4-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8000000000000004i2−4i24i2−4i24-44-40000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ9488-8-8000000000000004i2−4i24i2−4i2-44-44000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ9588-8-800000000000000−4i24i2−4i24i24-44-4000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ9688-8-800000000000000−4i24i2−4i24i2-44-440000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ978-88-8000000000000004i2−4i2−4i24i24i−4i−4i4i000000000000−222222−220000000000000000000000000000000000000000000000000000000000
χ988-88-8000000000000004i2−4i2−4i24i2−4i4i4i−4i00000000000022−22−22220000000000000000000000000000000000000000000000000000000000
χ998-88-800000000000000−4i24i24i2−4i24i−4i−4i4i00000000000022−22−22220000000000000000000000000000000000000000000000000000000000
χ1008-88-800000000000000−4i24i24i2−4i2−4i4i4i−4i000000000000−222222−220000000000000000000000000000000000000000000000000000000000

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