Finite Group Databasebeta

← Group #11771554

Character table — Group #11771554

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888888888888888888888881818181818181818363636363636363636363636363636367272
order122244443344666666121212121212121288121212121212121224242424242424242424242424242424888888881616161616161616161616161616161624
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ511111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−iii−i−ii−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ461-1
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−iii−i−ii−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ461-1
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii−i−iii−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-11
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii−i−iii−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-11
χ131111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−iii−i−ii−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-11
χ141111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−iii−i−ii−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-11
χ151111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii−i−iii−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ261-1
χ161111-1-1-1-1111-1111111-1-1-1-1-1-1-1-1−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii−i−iii−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ261-1
χ172222222222-2-22222222222222200-2-2-2-2-2-2-2-2000000000000000022-2-2-2-222000000000000000000
χ182222222222-2-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-22222-2-2000000000000000000
χ192222-2-2-2-222-22222222-2-2-2-2-2-2-2-200-2-2-2-2222200000000000000002i−2i−2i−2i2i2i2i−2i000000000000000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-200-2-2-2-222220000000000000000−2i2i2i2i−2i−2i−2i2i000000000000000000
χ2122-2-22i−2i2i−2i220022-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ4100
χ2222-2-22i−2i2i−2i220022-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ4100
χ2322-2-22i−2i2i−2i220022-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ4100
χ2422-2-22i−2i2i−2i220022-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ4100
χ2522-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000000000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ4700
χ2622-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000000000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ4700
χ2722-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000000000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ4700
χ2822-2-2−2i2i−2i2i220022-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000000000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ4700
χ292-2-2222-2-22200-2-222-2-22222-2-2-2-2000000000000000000000000002i−2i0000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ302-2-2222-2-22200-2-222-2-22222-2-2-2-2000000000000000000000000002i−2i0000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ312-2-2222-2-22200-2-222-2-22222-2-2-2-200000000000000000000000000−2i2i00002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ322-2-2222-2-22200-2-222-2-22222-2-2-2-200000000000000000000000000−2i2i00002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ332-2-22-2-2222200-2-222-2-2-2-2-2-2222200000000000000000000000000220000-2-2−i2i2i2−i2i2−i2−i2i20000000000
χ342-2-22-2-2222200-2-222-2-2-2-2-2-2222200000000000000000000000000220000-2-2i2−i2−i2i2−i2i2i2−i20000000000
χ352-2-22-2-2222200-2-222-2-2-2-2-2-2222200000000000000000000000000-2-20000222−2−222−2−220000000000
χ362-2-22-2-2222200-2-222-2-2-2-2-2-2222200000000000000000000000000-2-2000022−222−2−222−20000000000
χ37444444441-2441-21-21-21-21-21-21-24411-2-211-2-21111-2-2-2-21111-2-2-2-200000000000000000000000000
χ38444444441-2441-21-21-21-21-21-21-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-1222200000000000000000000000000
χ39444444441-2-4-41-21-21-21-21-21-21-200-1-122-1-12233-3-3000033-3-3000000000000000000000000000000
χ40444444441-2-4-41-21-21-21-21-21-21-200-1-122-1-122-3-3330000-3-333000000000000000000000000000000
χ4144444444-2144-21-21-21-21-21-21-2144-2-211-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ4244444444-2144-21-21-21-21-21-21-21-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000
χ4344444444-21-4-4-21-21-21-21-21-21-210022-1-122-1-1000033-3-3000033-3-300000000000000000000000000
χ4444444444-21-4-4-21-21-21-21-21-21-210022-1-122-1-10000-3-3330000-3-33300000000000000000000000000
χ454444-4-4-4-41-24-41-21-21-2-12-12-12-124i−4i11-2-2-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i00000000000000000000000000
χ464444-4-4-4-41-24-41-21-21-2-12-12-12-12−4i4i11-2-2-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i00000000000000000000000000
χ474444-4-4-4-41-2-441-21-21-2-12-12-12-1200-1-12211-2-23i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ484444-4-4-4-41-2-441-21-21-2-12-12-12-1200-1-12211-2-2−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ494444-4-4-4-4-214-4-21-21-212-12-12-12-14i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i00000000000000000000000000
χ504444-4-4-4-4-214-4-21-21-212-12-12-12-1−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii00000000000000000000000000
χ514444-4-4-4-4-21-44-21-21-212-12-12-12-10022-1-1-2-21100003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000
χ524444-4-4-4-4-21-44-21-21-212-12-12-12-10022-1-1-2-2110000−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000
χ534-44-44i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i003-3003i−3i00ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26002ζ10−2ζ26−2ζ10+2ζ26−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ4600−2ζ14+2ζ462ζ14−2ζ4600000000000000000000000000
χ544-44-44i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i003-3003i−3i00−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ2600−2ζ10+2ζ262ζ10−2ζ26ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ46002ζ14−2ζ46−2ζ14+2ζ4600000000000000000000000000
χ554-44-44i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i00-3300−3i3i00ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ262ζ10−2ζ26−2ζ10+2ζ2600−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−2ζ14+2ζ462ζ14−2ζ460000000000000000000000000000
χ564-44-44i−4i−4i4i1-200-12-121-2i−2i−i2i−i2ii−2i00-3300−3i3i00−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−2ζ10+2ζ262ζ10−2ζ2600ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ462ζ14−2ζ46−2ζ14+2ζ460000000000000000000000000000
χ574-44-44i−4i−4i4i4400-4-4-4-4444i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ584-44-44i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii00003-3003i−3i002ζ10−2ζ26−2ζ10+2ζ26ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ2600−2ζ14+2ζ462ζ14−2ζ46−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ4600000000000000000000000000
χ594-44-44i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii00003-3003i−3i00−2ζ10+2ζ262ζ10−2ζ26−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26002ζ14−2ζ46−2ζ14+2ζ46ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ4600000000000000000000000000
χ604-44-44i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii0000-3300−3i3i2ζ10−2ζ26−2ζ10+2ζ2600−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ26−2ζ14+2ζ462ζ14−2ζ4600ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ4600000000000000000000000000
χ614-44-44i−4i−4i4i-21002-12-1-21−2ii2i−i2i−i−2ii0000-3300−3i3i−2ζ10+2ζ262ζ10−2ζ2600ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ262ζ14−2ζ46−2ζ14+2ζ4600−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ4600000000000000000000000000
χ624-44-4−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i003-300−3i3i00−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ4600−2ζ14+2ζ462ζ14−2ζ46ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ26002ζ10−2ζ26−2ζ10+2ζ2600000000000000000000000000
χ634-44-4−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i003-300−3i3i00ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ46002ζ14−2ζ46−2ζ14+2ζ46−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ2600−2ζ10+2ζ262ζ10−2ζ2600000000000000000000000000
χ644-44-4−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i00-33003i−3i00−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−2ζ14+2ζ462ζ14−2ζ4600ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ262ζ10−2ζ26−2ζ10+2ζ260000000000000000000000000000
χ654-44-4−4i4i4i−4i1-200-12-121-2−i2ii−2ii−2i−i2i00-33003i−3i00ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ462ζ14−2ζ46−2ζ14+2ζ4600−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−2ζ10+2ζ262ζ10−2ζ260000000000000000000000000000
χ664-44-4−4i4i4i−4i4400-4-4-4-444−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ674-44-4−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i00003-300−3i3i00−2ζ14+2ζ462ζ14−2ζ46−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46002ζ10−2ζ26−2ζ10+2ζ26ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ2600000000000000000000000000
χ684-44-4−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i00003-300−3i3i002ζ14−2ζ46−2ζ14+2ζ46ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ4600−2ζ10+2ζ262ζ10−2ζ26−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ2600000000000000000000000000
χ694-44-4−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i0000-33003i−3i−2ζ14+2ζ462ζ14−2ζ4600ζ14−ζ46−ζ14+ζ46ζ14−ζ46−ζ14+ζ462ζ10−2ζ26−2ζ10+2ζ2600−ζ10+ζ26ζ10−ζ26−ζ10+ζ26ζ10−ζ2600000000000000000000000000
χ704-44-4−4i4i4i−4i-21002-12-1-212i−i−2ii−2ii2i−i0000-33003i−3i2ζ14−2ζ46−2ζ14+2ζ4600−ζ14+ζ46ζ14−ζ46−ζ14+ζ46ζ14−ζ46−2ζ10+2ζ262ζ10−2ζ2600ζ10−ζ26−ζ10+ζ26ζ10−ζ26−ζ10+ζ2600000000000000000000000000
χ7188-8-88i−8i8i−8i2-4002-4-24-242i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ7288-8-88i−8i8i−8i-4200-424-24-2−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ7388-8-8−8i8i−8i8i2-4002-4-24-24−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ7488-8-8−8i8i−8i8i-4200-424-24-24i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ758-8-8888-8-82-400-242-4-242-42-4-24-240000000000000000000000000000000000000000000000000000
χ768-8-8888-8-8-42004-2-424-2-42-424-24-20000000000000000000000000000000000000000000000000000
χ778-8-88-8-8882-400-242-4-24-24-242-42-40000000000000000000000000000000000000000000000000000
χ788-8-88-8-888-42004-2-424-24-24-2-42-420000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.