Finite Group Databasebeta

← Group #11791373

Character table — Group #11791373

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444444444444666666666666888888888888888812121212121212121212121212121212121224242424242424242424242472727272
order1222223344446666661212121236666666888812121212121212121212242424242424242488882424242424242424661212242424242424242424242424444488121212121212121224242424448812121212242424244488
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
χ5111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ91-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-11-1iiiiii−i−i−i−i−i−iii−i−i1-1iiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ101-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-11-1iiiiii−i−i−i−i−i−iii−i−i1-1iiii−i−i−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ111-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-111111-11-1iiiiii−i−i−i−i−i−i−i−iii-11−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ121-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-111111-11-1iiiiii−i−i−i−i−i−i−i−iii-11−i−i−i−iiiii-1-111-11−ii-1-111−i−iii1-1i−i
χ131-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-11-1−i−i−i−i−i−iiiiiii−i−iii1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ141-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-11-1−i−i−i−i−i−iiiiiii−i−iii1-1−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i-11i−i
χ151-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-111111-11-1−i−i−i−i−i−iiiiiiiii−i−i-11iiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ161-1-111-1111-11-1-1-11-1-11-1-111111-1-1-1-11−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-111111-11-1−i−i−i−i−i−iiiiiiiii−i−i-11iiii−i−i−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ1722222222-2-2-2-2222222-2-2-2-2222222222i−2i2i−2i-2-2-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000022-2-22i2i2i−2i−2i−2i2i2i2i−2i−2i−2i0000000000000000000000000000000000
χ1822222222-2-2-2-2222222-2-2-2-222222222−2i2i−2i2i-2-2-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000022-2-2−2i−2i−2i2i2i2i−2i−2i−2i2i2i2i0000000000000000000000000000000000
χ192222222-1222222-1-1-12-1-1-1-1-12-12-1-1-1-12222-1-122-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222-1222222-1-1-12-1-1-1-1-12-12-1-1-1-12222-1-122-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-12-1-12-1-12-1-12-1-1-2-2-2-2-2-21111111111110000000000000000
χ212222222-1222222-1-1-12-1-1-1-1-12-12-1-1-1-1-2-2-2-2-1-122-1-12-1-12111111112222-1-1-1-1-1-1-1-1-1-1-1-1-211-211-211-211-2-2-2-22211111111-1-1-1-10000000000000000
χ222222222-1222222-1-1-12-1-1-1-1-12-12-1-1-1-1-2-2-2-2-1-122-1-12-1-1211111111-2-2-2-211111111-1-1-1-1-211-211-211-2112222-2-2-1-1-1-1-1-1-1-111110000000000000000
χ232222222-1-2-2-2-222-1-1-121111-12-12-1-1-1-12i−2i2i−2i11-2-211-211-2−i−iii−i−iii000033−3−333−3−3-1-1112i−i−i−2iii2i−i−i−2iii000000−i3−i3i3i3−i3−i3i3i33−33−30000000000000000
χ242222222-1-2-2-2-222-1-1-121111-12-12-1-1-1-12i−2i2i−2i11-2-211-211-2−i−iii−i−iii0000−3−333−3−333-1-1112i−i−i−2iii2i−i−i−2iii000000i3i3−i3−i3i3i3−i3−i3−33−330000000000000000
χ252222222-1-2-2-2-222-1-1-121111-12-12-1-1-1-1−2i2i−2i2i11-2-211-211-2ii−i−iii−i−i000033−3−333−3−3-1-111−2iii2i−i−i−2iii2i−i−i000000i3i3−i3−i3i3i3−i3−i33−33−30000000000000000
χ262222222-1-2-2-2-222-1-1-121111-12-12-1-1-1-1−2i2i−2i2i11-2-211-211-2ii−i−iii−i−i0000−3−333−3−333-1-111−2iii2i−i−i−2iii2i−i−i000000−i3−i3i3i3−i3−i3i3i3−33−330000000000000000
χ27222222-122222-1-1222-12222-1-12-12-1-1-1222222-1-1-1-1-1-1-1-122222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ28222222-122222-1-1222-12222-1-12-12-1-1-1222222-1-1-1-1-1-1-1-122222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ29222222-122222-1-1222-12222-1-12-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2000000000000-1-1-1-111111111111100000000000000000022-2-2-1-1-1-111110000
χ30222222-122222-1-1222-12222-1-12-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2000000000000-1-1-1-1111111111111000000000000000000-2-2221111-1-1-1-10000
χ31222222-12-2-2-2-2-1-1222-1-2-2-2-2-1-12-12-1-1-12i−2i2i−2i-2-2111111112i2i−2i−2i2i2i−2i−2i000000000000-1-111−i−i−iiii−i−i−iiii0000000000000000000000−i3i3−i3i33−33−30000
χ32222222-12-2-2-2-2-1-1222-1-2-2-2-2-1-12-12-1-1-12i−2i2i−2i-2-2111111112i2i−2i−2i2i2i−2i−2i000000000000-1-111−i−i−iiii−i−i−iiii0000000000000000000000i3−i3i3−i3−33−330000
χ33222222-12-2-2-2-2-1-1222-1-2-2-2-2-1-12-12-1-1-1−2i2i−2i2i-2-211111111−2i−2i2i2i−2i−2i2i2i000000000000-1-111iii−i−i−iiii−i−i−i0000000000000000000000−i3i3−i3i3−33−330000
χ34222222-12-2-2-2-2-1-1222-1-2-2-2-2-1-12-12-1-1-1−2i2i−2i2i-2-211111111−2i−2i2i2i−2i−2i2i2i000000000000-1-111iii−i−i−iiii−i−i−i0000000000000000000000i3−i3i3−i33−33−30000
χ352222-2-2222-2-22222222-2-2-2-22-2-2-2-22220000222-2-2-2-2-2-2200000000000000000000-2-2220000000000002-22-2002-22-22-22-200000000000000000000
χ362222-2-2222-2-22222222-2-2-2-22-2-2-2-22220000222-2-2-2-2-2-2200000000000000000000-2-222000000000000-22-2200-22-22-22-2200000000000000000000
χ372222-2-222-222-222222222222-2-2-2-22220000-2-2-2222222-200000000222222222222-2-2-2-20000000000000000-2-200000000-2-2-2-20000000000000000
χ382222-2-222-222-222222222222-2-2-2-22220000-2-2-2222222-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000220000000022220000000000000000
χ392222-2-22-12-2-2222-1-1-121111-1-21-21-1-1-10000-1-12-211-21123−33−33−33−3000033−3−333−3−311-1-103−303−303−303−32-22-200-11-11-11-11−33−330000000000000000
χ402222-2-22-12-2-2222-1-1-121111-1-21-21-1-1-10000-1-12-211-21123−33−33−33−30000−3−333−3−33311-1-103−303−303−303−3-22-22001-11-11-11-13−33−30000000000000000
χ412222-2-22-12-2-2222-1-1-121111-1-21-21-1-1-10000-1-12-211-2112−33−33−33−33000033−3−333−3−311-1-10−330−330−330−33-22-22001-11-11-11-1−33−330000000000000000
χ422222-2-22-12-2-2222-1-1-121111-1-21-21-1-1-10000-1-12-211-2112−33−33−33−330000−3−333−3−33311-1-10−330−330−330−332-22-200-11-11-11-113−33−30000000000000000
χ432222-2-22-1-222-222-1-1-12-1-1-1-1-1-21-21-1-1-1000011-22-1-12-1-1-2−i3i3i3−i3−i3i3i3−i32222-1-1-1-1-1-1-1-111110−i3i30i3−i30−i3i30i3−i30000-2-2−i3i3i3−i3−i3i3i3−i311110000000000000000
χ442222-2-22-1-222-222-1-1-12-1-1-1-1-1-21-21-1-1-1000011-22-1-12-1-1-2−i3i3i3−i3−i3i3i3−i3-2-2-2-21111111111110−i3i30i3−i30−i3i30i3−i3000022i3−i3−i3i3i3−i3−i3i3-1-1-1-10000000000000000
χ452222-2-22-1-222-222-1-1-12-1-1-1-1-1-21-21-1-1-1000011-22-1-12-1-1-2i3−i3−i3i3i3−i3−i3i32222-1-1-1-1-1-1-1-111110i3−i30−i3i30i3−i30−i3i30000-2-2i3−i3−i3i3i3−i3−i3i311110000000000000000
χ462222-2-22-1-222-222-1-1-12-1-1-1-1-1-21-21-1-1-1000011-22-1-12-1-1-2i3−i3−i3i3i3−i3−i3i3-2-2-2-21111111111110i3−i30−i3i30i3−i30−i3i3000022−i3i3i3−i3−i3i3i3−i3-1-1-1-10000000000000000
χ472-2-222-222-22-22-2-22-2-2222-2-2222-2-2-2-222-2-22-22-2-2-2-2222222-2-2-2-2220000000000002-2-22222-2-2-2-2-2-22220000000000000000000000000000000000
χ482-2-222-222-22-22-2-22-2-2222-2-2222-2-2-2-22-222-2-22-2-2-2-22222-2-22222-2-20000000000002-2-22-2-2-2222222-2-2-20000000000000000000000000000000000
χ492-2-222-22-12-22-2-2-2-111211-1-1-12-1-2111-12i2i−2i−2i-1122-1-1-211-2−i−i−i−iiiii22-2-2-1-1-1-11111-11-112i−i−i2i−i−i−2iii−2iii2i2i−2i−2i2-2−i−i−i−iiiii-1-1110000000000000000
χ502-2-222-22-12-22-2-2-2-111211-1-1-12-1-2111-12i2i−2i−2i-1122-1-1-211-2−i−i−i−iiiii-2-2221111-1-1-1-1-11-112i−i−i2i−i−i−2iii−2iii−2i−2i2i2i-22iiii−i−i−i−i11-1-10000000000000000
χ512-2-222-22-12-22-2-2-2-111211-1-1-12-1-2111-1−2i−2i2i2i-1122-1-1-211-2iiii−i−i−i−i22-2-2-1-1-1-11111-11-11−2iii−2iii2i−i−i2i−i−i−2i−2i2i2i2-2iiii−i−i−i−i-1-1110000000000000000
χ522-2-222-22-12-22-2-2-2-111211-1-1-12-1-2111-1−2i−2i2i2i-1122-1-1-211-2iiii−i−i−i−i-2-2221111-1-1-1-1-11-11−2iii−2iii2i−i−i2i−i−i2i2i−2i−2i-22−i−i−i−iiiii11-1-10000000000000000
χ532-2-222-22-1-22-22-2-2-1112-1-111-12-1-2111-12-2-221-1-2-2112-1-12-1-11111-1-1000033−3−3−3−333-111-12-1-1-211-2112-1-1000000−3−33333−3−33−3−330000000000000000
χ542-2-222-22-1-22-22-2-2-1112-1-111-12-1-2111-12-2-221-1-2-2112-1-12-1-11111-1-10000−3−33333−3−3-111-12-1-1-211-2112-1-100000033−3−3−3−333−333−30000000000000000
χ552-2-222-22-1-22-22-2-2-1112-1-111-12-1-2111-1-222-21-1-2-2112-1-1211-1-1-1-111000033−3−3−3−333-111-1-2112-1-12-1-1-21100000033−3−3−3−3333−3−330000000000000000
χ562-2-222-22-1-22-22-2-2-1112-1-111-12-1-2111-1-222-21-1-2-2112-1-1211-1-1-1-1110000−3−33333−3−3-111-1-2112-1-12-1-1-211000000−3−33333−3−3−333−30000000000000000
χ572-2-222-2-122-22-2112-2-2-1-2-222-1-121-211-12i2i−2i−2i2-2-1-1-1-111112i2i2i2i−2i−2i−2i−2i000000000000-11-11−i−i−i−i−i−iiiiiii0000000000000000002-22i−2i-1-111−i−iii0000
χ582-2-222-2-122-22-2112-2-2-1-2-222-1-121-211-12i2i−2i−2i2-2-1-1-1-111112i2i2i2i−2i−2i−2i−2i000000000000-11-11−i−i−i−i−i−iiiiiii000000000000000000-22−2i2i11-1-1ii−i−i0000
χ592-2-222-2-122-22-2112-2-2-1-2-222-1-121-211-1−2i−2i2i2i2-2-1-1-1-11111−2i−2i−2i−2i2i2i2i2i000000000000-11-11iiiiii−i−i−i−i−i−i0000000000000000002-2−2i2i-1-111ii−i−i0000
χ602-2-222-2-122-22-2112-2-2-1-2-222-1-121-211-1−2i−2i2i2i2-2-1-1-1-11111−2i−2i−2i−2i2i2i2i2i000000000000-11-11iiiiii−i−i−i−i−i−i000000000000000000-222i−2i11-1-1−i−iii0000
χ612-2-222-2-12-22-22112-2-2-122-2-2-1-121-211-12-2-22-221111-1-1-1-122-2-2-2-222000000000000-111-1-1-1-1111111-1-1-10000000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ622-2-222-2-12-22-22112-2-2-122-2-2-1-121-211-12-2-22-221111-1-1-1-122-2-2-2-222000000000000-111-1-1-1-1111111-1-1-10000000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ632-2-222-2-12-22-22112-2-2-122-2-2-1-121-211-1-222-2-221111-1-1-1-1-2-22222-2-2000000000000-111-1111-1-1-1-1-1-11110000000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ642-2-222-2-12-22-22112-2-2-122-2-2-1-121-211-1-222-2-221111-1-1-1-1-2-22222-2-2000000000000-111-1111-1-1-1-1-1-11110000000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ652-2-22-222222-2-2-2-22-2-2222-2-22-2-222-2-2200002-22-2-2-2222-200000000000000000000-222-20000000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ662-2-22-222222-2-2-2-22-2-2222-2-22-2-222-2-2200002-22-2-2-2222-200000000000000000000-222-2000000000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ672-2-22-2222-2-222-2-22-2-22-2-2222-2-222-2-220000-22-2222-2-2-220000000022-2-22222-2-2-2-2-22-220000000000000000-2200000000-2-2220000000000000000
χ682-2-22-2222-2-222-2-22-2-22-2-2222-2-222-2-220000-22-2222-2-2-2200000000-2-222-2-2-2-22222-22-2200000000000000002-20000000022-2-20000000000000000
χ692-2-22-222-122-2-2-2-2-1112-1-111-1-212-111-10000-112-2112-1-1-2−i3i3−i3i3i3−i3i3−i3000033−3−3−3−3331-1-110−i3i30−i3i30i3−i30i3−i3−2i2i2i−2i00i−ii−i−ii−ii−333−30000000000000000
χ702-2-22-222-122-2-2-2-2-1112-1-111-1-212-111-10000-112-2112-1-1-2−i3i3−i3i3i3−i3i3−i30000−3−33333−3−31-1-110−i3i30−i3i30i3−i30i3−i32i−2i−2i2i00−ii−iii−ii−i3−3−330000000000000000
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χ8944-4-4004-200004-42-22-423−2323−23-20000-2220000000023−23023−2300000000022−2222−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000000000
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χ1004-4-444-4-2-24-44-422-222-222-2-21-2-222-1-11−4i−4i4i4i-22-2-2112-1-122i2i2i2i−2i−2i−2i−2i0000000000001-11-12i−i−i2i−i−i−2iii−2iii0000000000000000000000000000000000
χ1014-4-444-4-2-2-44-4422-222-2-2-2221-2-222-1-114-4-442-222-1-1-211-2-2-22222-2-20000000000001-1-11-2112-1-12-1-1-2110000000000000000000000000000000000
χ1024-4-444-4-2-2-44-4422-222-2-2-2221-2-222-1-11-444-42-222-1-1-211-222-2-2-2-2220000000000001-1-112-1-1-211-2112-1-10000000000000000000000000000000000
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χ1084-4-44-44-2-2-4-44422-222-222-2-2122-2-2-1-1100002-22-2112-1-1-2−232323−2323−23−2323000000000000-11-1103−30−330−3303−30000000000000000000000000000000000
χ10988-8-800-480000-44-88-840000-40000-444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-800-4-40000-444-44443−4343−43200002-2-200000000−23230−232300000000000000000000000000000000000000000000000000000000000000000000000
χ11188-8-800-4-40000-444-444−4343−4343200002-2-20000000023−23023−2300000000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-800-4800004-4-8-8840000-400004-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-800-4-400004-444-4443−43−434320000-22-20000000023−230−232300000000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-800-4-400004-444-44−434343−4320000-22-200000000−2323023−2300000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.