Finite Group Databasebeta

← Group #11791381

Character table — Group #11791381

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444444444444666666666666888888888888888812121212121212121212121212121212121224242424242424242424242472727272
order1222223344446666661212121234444666666612121212121212121212121212121212121288882424242424242424661212121212121212121212121212888888242424242424242424242424448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91-1-111-11111-1-11-1-1-1-1111-1-11ii−i−i11-1-11-1-11-1iiii−i−i−i−i11-111-1-1-111-1-11111-1-1-1-11-1ii−i−i1-1iiii−i−i−i−i1-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101-1-111-11111-1-11-1-1-1-1111-1-11ii−i−i11-1-11-1-11-1iiii−i−i−i−i11-111-1-1-111-1-11111-1-1-1-11-1ii−i−i1-1iiii−i−i−i−i1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111-1-111-11111-1-11-1-1-1-1111-1-11ii−i−i11-1-11-1-11-1iiii−i−i−i−i11-111-1-1-1-1-111-1-1-1-111111-1ii−i−i1-1iiii−i−i−i−i-11−i−iii-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121-1-111-11111-1-11-1-1-1-1111-1-11ii−i−i11-1-11-1-11-1iiii−i−i−i−i11-111-1-1-1-1-111-1-1-1-111111-1ii−i−i1-1iiii−i−i−i−i-11−i−iii-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131-1-111-11111-1-11-1-1-1-1111-1-11−i−iii11-1-11-1-11-1−i−i−i−iiiii11-111-1-1-111-1-11111-1-1-1-11-1−i−iii1-1−i−i−i−iiiii1-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141-1-111-11111-1-11-1-1-1-1111-1-11−i−iii11-1-11-1-11-1−i−i−i−iiiii11-111-1-1-111-1-11111-1-1-1-11-1−i−iii1-1−i−i−i−iiiii1-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151-1-111-11111-1-11-1-1-1-1111-1-11−i−iii11-1-11-1-11-1−i−i−i−iiiii11-111-1-1-1-1-111-1-1-1-111111-1−i−iii1-1−i−i−i−iiiii-11ii−i−i-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161-1-111-11111-1-11-1-1-1-1111-1-11−i−iii11-1-11-1-11-1−i−i−i−iiiii11-111-1-1-1-1-111-1-1-1-111111-1−i−iii1-1−i−i−i−iiiii-11ii−i−i-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ1722222222-2-2-2-2222222-2-2-2-2200002222222-2-200000000-2-2-2-2-2-2-2-2000000000000220000-2-200000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000
χ1822222222-2-2-2-2222222-2-2-2-2200002222222-2-200000000-2-2-2-2-2-2-2-2000000000000220000-2-20000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222-12222222-1-1-12222-122222-12-1-1-1-12222222222-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ202222222-12222222-1-1-12222-122222-12-1-1-1-12222222222-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ212222222-12222222-1-1-12222-1-2-2-2-22-12-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000000000-1-11111-1-11111111100000000000000000022-2-2-1-1-1-111110000
χ222222222-12222222-1-1-12222-1-2-2-2-22-12-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000000000-1-11111-1-111111111000000000000000000-2-2221111-1-1-1-10000
χ23222222-122222-1-1-1222-1-1-1-1-12222-12-12-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ24222222-122222-1-1-1222-1-1-1-1-12222-12-12-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-12-2-2-2-211111111-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111110000000000000000
χ25222222-122222-1-1-1222-1-1-1-1-1-2-2-2-2-12-12-1-1-1-1-111111111222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-2-2-1-1-1-1111111110000000000000000
χ26222222-122222-1-1-1222-1-1-1-1-1-2-2-2-2-12-12-1-1-1-1-111111111222-1-1-1-12-2-2-2-211111111-1-1-2-2-2-2-1-111111111-2-222221111-1-1-1-1-1-1-1-10000000000000000
χ27222222-12-2-2-2-2-1-1-12221111-10000-12-12-1-1-111−i3−i3i3i3−i3−i3i3i3-2-2-21111-2000033−3−333−3−3-1-1000011−i3−i3i3i3−i3−i3i3i3002i−2i2i−2i3−33−3−i−iii−i−iii0000000000000000
χ28222222-12-2-2-2-2-1-1-12221111-10000-12-12-1-1-111−i3−i3i3i3−i3−i3i3i3-2-2-21111-20000−3−333−3−333-1-1000011−i3−i3i3i3−i3−i3i3i300−2i2i−2i2i−33−33ii−i−iii−i−i0000000000000000
χ29222222-12-2-2-2-2-1-1-12221111-10000-12-12-1-1-111i3i3−i3−i3i3i3−i3−i3-2-2-21111-2000033−3−333−3−3-1-1000011i3i3−i3−i3i3i3−i3−i300−2i2i−2i2i3−33−3ii−i−iii−i−i0000000000000000
χ30222222-12-2-2-2-2-1-1-12221111-10000-12-12-1-1-111i3i3−i3−i3i3i3−i3−i3-2-2-21111-20000−3−333−3−333-1-1000011i3i3−i3−i3i3i3−i3−i3002i−2i2i−2i−33−33−i−iii−i−iii0000000000000000
χ312222-2-2222-2-22222222-2-2-2-222-22-2-2-2-2-2222222-22-22-22-22-2-2-2-2-2-22000000000000-2-22-22-2222-22-22-22-20000000000000000000000000000000000
χ322222-2-2222-2-22222222-2-2-2-22-22-22-2-2-2-222222-22-22-22-222-2-2-2-2-2-22000000000000-2-2-22-2222-22-22-22-220000000000000000000000000000000000
χ332222-2-222-222-2222222222220000-2-2-2-2222-2-200000000-2222222-2222222222222-2-20000-2-200000000-2-20000-2-2-2-2000000000000000000000000
χ342222-2-222-222-2222222222220000-2-2-2-2222-2-200000000-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-2000000002200002222000000000000000000000000
χ352222-2-22-12-2-22222-1-1-1-2-2-2-2-12-22-2-21-21-1-1-1222-22-22-22-2-1111111-100000000000011-11-11-1-1-11-11-11-110000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ362222-2-22-12-2-22222-1-1-1-2-2-2-2-12-22-2-21-21-1-1-1222-22-22-22-2-1111111-100000000000011-11-11-1-1-11-11-11-110000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ372222-2-22-12-2-22222-1-1-1-2-2-2-2-1-22-22-21-21-1-1-122-22-22-22-22-1111111-1000000000000111-11-1-1-11-11-11-11-10000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ382222-2-22-12-2-22222-1-1-1-2-2-2-2-1-22-22-21-21-1-1-122-22-22-22-22-1111111-1000000000000111-11-1-1-11-11-11-11-10000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ392222-2-2-122-2-22-1-1-12221111-12-22-21-21-2-1-1-1-1-1-11-11-11-112-2-211112000033−3−333−3−3112-22-2-1-1-11-11-11-11000000−33−333−33−33−33−30000000000000000
χ402222-2-2-122-2-22-1-1-12221111-12-22-21-21-2-1-1-1-1-1-11-11-11-112-2-2111120000−3−333−3−333112-22-2-1-1-11-11-11-110000003−33−3−33−33−33−330000000000000000
χ412222-2-2-122-2-22-1-1-12221111-1-22-221-21-2-1-1-1-1-11-11-11-11-12-2-211112000033−3−333−3−311-22-22-1-11-11-11-11-1000000−33−33−33−33−33−330000000000000000
χ422222-2-2-122-2-22-1-1-12221111-1-22-221-21-2-1-1-1-1-11-11-11-11-12-2-2111120000−3−333−3−33311-22-22-1-11-11-11-11-10000003−33−33−33−33−33−30000000000000000
χ432222-2-2-12-222-2-1-1-1222-1-1-1-1-100001-21-2-1-1-111−i3i3i3−i3−i3i3i3−i3-222-1-1-1-1-22222-1-1-1-1-1-1-1-111000011−i3i3i3−i3−i3i3i3−i3-2-200001111−i3i3i3−i3−i3i3i3−i30000000000000000
χ442222-2-2-12-222-2-1-1-1222-1-1-1-1-100001-21-2-1-1-111−i3i3i3−i3−i3i3i3−i3-222-1-1-1-1-2-2-2-2-21111111111000011−i3i3i3−i3−i3i3i3−i3220000-1-1-1-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ452222-2-2-12-222-2-1-1-1222-1-1-1-1-100001-21-2-1-1-111i3−i3−i3i3i3−i3−i3i3-222-1-1-1-1-22222-1-1-1-1-1-1-1-111000011i3−i3−i3i3i3−i3−i3i3-2-200001111i3−i3−i3i3i3−i3−i3i30000000000000000
χ462222-2-2-12-222-2-1-1-1222-1-1-1-1-100001-21-2-1-1-111i3−i3−i3i3i3−i3−i3i3-222-1-1-1-1-2-2-2-2-21111111111000011i3−i3−i3i3i3−i3−i3i3220000-1-1-1-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ472-2-222-222-2-2222-2-2-2-22-2-2222000022-2-22-2-2-2200000000-2-22-2-22220000000000002-20000-2200000000002-2-22000022-2-2-2-2220000000000000000
χ482-2-222-222-2-2222-2-2-2-22-2-2222000022-2-22-2-2-2200000000-2-22-2-22220000000000002-20000-220000000000-222-20000-2-22222-2-20000000000000000
χ492-2-222-22-122-2-22-2-211-122-2-2-12i2i−2i−2i2-1-21-1112-22i2i2i2i−2i−2i−2i−2i-1-11-1-1111000000000000-11−i−iii-11−i−i−i−iiiii0000000000000000002-22i−2i-1-111−i−iii0000
χ502-2-222-22-122-2-22-2-211-122-2-2-12i2i−2i−2i2-1-21-1112-22i2i2i2i−2i−2i−2i−2i-1-11-1-1111000000000000-11−i−iii-11−i−i−i−iiiii000000000000000000-22−2i2i11-1-1ii−i−i0000
χ512-2-222-22-122-2-22-2-211-122-2-2-1−2i−2i2i2i2-1-21-1112-2−2i−2i−2i−2i2i2i2i2i-1-11-1-1111000000000000-11ii−i−i-11iiii−i−i−i−i0000000000000000002-2−2i2i-1-111ii−i−i0000
χ522-2-222-22-122-2-22-2-211-122-2-2-1−2i−2i2i2i2-1-21-1112-2−2i−2i−2i−2i2i2i2i2i-1-11-1-1111000000000000-11ii−i−i-11iiii−i−i−i−i000000000000000000-222i−2i11-1-1−i−iii0000
χ532-2-222-2-1222-2-2-111-2-22-1-111-12i2i−2i−2i-121-2-111-11−i−i−i−iiiii22-2-1-111-222-2-2-1-1-1-11111-112i2i−2i−2i-11−i−i−i−iiiii2-22i2i−2i−2i-1-111−i−i−i−iiiii0000000000000000
χ542-2-222-2-1222-2-2-111-2-22-1-111-12i2i−2i−2i-121-2-111-11−i−i−i−iiiii22-2-1-111-2-2-2221111-1-1-1-1-112i2i−2i−2i-11−i−i−i−iiiii-22−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000000000
χ552-2-222-2-1222-2-2-111-2-22-1-111-1−2i−2i2i2i-121-2-111-11iiii−i−i−i−i22-2-1-111-222-2-2-1-1-1-11111-11−2i−2i2i2i-11iiii−i−i−i−i2-2−2i−2i2i2i-1-111iiii−i−i−i−i0000000000000000
χ562-2-222-2-1222-2-2-111-2-22-1-111-1−2i−2i2i2i-121-2-111-11iiii−i−i−i−i22-2-1-111-2-2-2221111-1-1-1-1-11−2i−2i2i2i-11iiii−i−i−i−i-222i2i−2i−2i11-1-1−i−i−i−iiiii0000000000000000
χ572-2-222-2-12-2-222-111-2-2211-1-1-10000-121-2-1111-133−3−3−3−333-2-2211-1-12000033−3−3−3−333-1100001-133−3−3−3−33300-222-23−3−3311-1-1-1-1110000000000000000
χ582-2-222-2-12-2-222-111-2-2211-1-1-10000-121-2-1111-133−3−3−3−333-2-2211-1-120000−3−33333−3−3-1100001-133−3−3−3−333002-2-22−333−3-1-11111-1-10000000000000000
χ592-2-222-2-12-2-222-111-2-2211-1-1-10000-121-2-1111-1−3−33333−3−3-2-2211-1-12000033−3−3−3−333-1100001-1−3−33333−3−3002-2-223−3−33-1-11111-1-10000000000000000
χ602-2-222-2-12-2-222-111-2-2211-1-1-10000-121-2-1111-1−3−33333−3−3-2-2211-1-120000−3−33333−3−3-1100001-1−3−33333−3−300-222-2−333−311-1-1-1-1110000000000000000
χ612-2-22-22222-22-22-2-2-2-22-2-22222i−2i−2i2i-2-2222-2-22-22i−2i2i−2i−2i2i−2i2i2-22-2-222-2000000000000-222i−2i−2i2i2-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000
χ622-2-22-22222-22-22-2-2-2-22-2-2222−2i2i2i−2i-2-2222-2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2-222-2000000000000-22−2i2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000
χ632-2-22-2222-22-222-2-2-2-2222-2-220000-2-2222-2-2-2200000000-22-222-2-2222-2-22222-2-2-2-2-220000-2200000000-220000-2-222000000000000000000000000
χ642-2-22-2222-22-222-2-2-2-2222-2-220000-2-2222-2-2-2200000000-22-222-2-22-2-222-2-2-2-22222-220000-22000000002-2000022-2-2000000000000000000000000
χ652-2-22-222-12-22-22-2-211-1-2-222-12i−2i−2i2i-212-1-1112-22i−2i2i−2i−2i2i−2i2i-11-111-1-110000000000001-1−iii−i-11−ii−iii−ii−i0000000000000000000000−i3i3i3−i33−3−330000
χ662-2-22-222-12-22-22-2-211-1-2-222-12i−2i−2i2i-212-1-1112-22i−2i2i−2i−2i2i−2i2i-11-111-1-110000000000001-1−iii−i-11−ii−iii−ii−i0000000000000000000000i3−i3−i3i3−333−30000
χ672-2-22-222-12-22-22-2-211-1-2-222-1−2i2i2i−2i-212-1-1112-2−2i2i−2i2i2i−2i2i−2i-11-111-1-110000000000001-1i−i−ii-11i−ii−i−ii−ii0000000000000000000000−i3i3i3−i3−333−30000
χ682-2-22-222-12-22-22-2-211-1-2-222-1−2i2i2i−2i-212-1-1112-2−2i2i−2i2i2i−2i2i−2i-11-111-1-110000000000001-1i−i−ii-11i−ii−i−ii−ii0000000000000000000000i3−i3−i3i33−3−330000
χ692-2-22-22-122-22-2-111-2-2211-1-1-12i−2i−2i2i1-2-12-111-11−ii−iii−ii−i2-2211-1-1-2000033−3−3−3−3331-12i−2i−2i2i-11−ii−iii−ii−i000000−333−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ702-2-22-22-122-22-2-111-2-2211-1-1-12i−2i−2i2i1-2-12-111-11−ii−iii−ii−i2-2211-1-1-20000−3−33333−3−31-12i−2i−2i2i-11−ii−iii−ii−i0000003−3−33−i3i3−i3i3i3−i3i3−i30000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.