Finite Group Databasebeta

← Group #11788627

Character table — Group #11788627

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444444444444666666666666888888888888888812121212121212121212121212121212121224242424242424242424242472727272
order122222334444666666121212123666666688881212121212121212121224242424242424248888242424242424242466121224242424242424242424242422446666881212121224242424448812121212242424242288
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
χ5111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ91-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11ii−i−i1-11-111-1-1-11iiii−i−i−i−iii−i−iiiii−i−i−i−i1-11-1iiiiii−i−i−i−i−i−i1-11-111-1-1i−i11-1-1ii−i−ii−i1-1ii−i−i11-1-11-1i−i
χ101-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11ii−i−i1-11-111-1-1-11iiii−i−i−i−iii−i−iiiii−i−i−i−i1-11-1iiiiii−i−i−i−i−i−i1-11-111-1-1i−i11-1-1ii−i−i−ii-11−i−iii-1-111-11−ii
χ111-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11ii−i−i1-11-111-1-1-11iiii−i−i−i−i−i−iii−i−i−i−iiiii1-11-1iiiiii−i−i−i−i−i−i-11-11-1-111−ii-1-111−i−iiii−i1-1ii−i−i11-1-1-11−ii
χ121-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11ii−i−i1-11-111-1-1-11iiii−i−i−i−i−i−iii−i−i−i−iiiii1-11-1iiiiii−i−i−i−i−i−i-11-11-1-111−ii-1-111−i−iii−ii-11−i−iii-1-1111-1i−i
χ131-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11−i−iii1-11-111-1-1-11−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-11-1−i−i−i−i−i−iiiiiii-11-11-1-111i−i-1-111ii−i−ii−i-11ii−i−i-1-1111-1−ii
χ141-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11−i−iii1-11-111-1-1-11−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-11-1−i−i−i−i−i−iiiiiii-11-11-1-111i−i-1-111ii−i−i−ii1-1−i−iii11-1-1-11i−i
χ151-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11−i−iii1-11-111-1-1-11−i−i−i−iiiii−i−iii−i−i−i−iiiii1-11-1−i−i−i−i−i−iiiiiii1-11-111-1-1−ii11-1-1−i−iiii−i-11ii−i−i-1-111-11i−i
χ161-11-11-11111-1-1-1-1-111-111-1-111-11-1-1-11−i−iii1-11-111-1-1-11−i−i−i−iiiii−i−iii−i−i−i−iiiii1-11-1−i−i−i−i−i−iiiiiii1-11-111-1-1−ii11-1-1−i−iii−ii1-1−i−iii11-1-11-1−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
χ192222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-1222222-1-1-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ202222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-1222222-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-12-1-12-1-12-1-12-1-1-2-2-2-21111-2-2111111110000000000000000
χ212222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-1-2-2-2-222-1-1-1-12-1-12111111112222-1-1-1-1-1-1-1-1-1-1-1-1-211-211-211-211-2-2-2-21111221111-1-1-1-10000000000000000
χ222222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-1-2-2-2-222-1-1-1-12-1-1211111111-2-2-2-211111111-1-1-1-1-211-211-211-2112222-1-1-1-1-2-2-1-1-1-111110000000000000000
χ232222222-1-2-2-2-22-1-12-121111-122-1-1-1-1-12i−2i2i−2i-2-21111-211-2−i−iii−i−iii000033−3−333−3−3-1-1112i−i−i−2iii2i−i−i−2iii0000−i3i3−i3i300−i3i3−i3i33−33−30000000000000000
χ242222222-1-2-2-2-22-1-12-121111-122-1-1-1-1-12i−2i2i−2i-2-21111-211-2−i−iii−i−iii0000−3−333−3−333-1-1112i−i−i−2iii2i−i−i−2iii0000i3−i3i3−i300i3−i3i3−i3−33−330000000000000000
χ252222222-1-2-2-2-22-1-12-121111-122-1-1-1-1-1−2i2i−2i2i-2-21111-211-2ii−i−iii−i−i000033−3−333−3−3-1-111−2iii2i−i−i−2iii2i−i−i0000i3−i3i3−i300i3−i3i3−i33−33−30000000000000000
χ262222222-1-2-2-2-22-1-12-121111-122-1-1-1-1-1−2i2i−2i2i-2-21111-211-2ii−i−iii−i−i0000−3−333−3−333-1-111−2iii2i−i−i−2iii2i−i−i0000−i3i3−i3i300−i3i3−i3i3−33−330000000000000000
χ27222222-122222-122-12-12222-1-1-122-1-1-12222-1-122-1-1-1-1-1-122222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ28222222-122222-122-12-12222-1-1-122-1-1-12222-1-122-1-1-1-1-1-122222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ29222222-122222-122-12-12222-1-1-122-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2000000000000-1-1-1-111111111111100000000000000000022-2-2-1-1-1-111110000
χ30222222-122222-122-12-12222-1-1-122-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2000000000000-1-1-1-1111111111111000000000000000000-2-2221111-1-1-1-10000
χ31222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-122-1-1-12i−2i2i−2i11-2-21111112i2i−2i−2i2i2i−2i−2i000000000000-1-111−i−i−iiii−i−i−iiii0000000000000000000000−i3i3−i3i33−33−30000
χ32222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-122-1-1-12i−2i2i−2i11-2-21111112i2i−2i−2i2i2i−2i−2i000000000000-1-111−i−i−iiii−i−i−iiii0000000000000000000000i3−i3i3−i3−33−330000
χ33222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-122-1-1-1−2i2i−2i2i11-2-2111111−2i−2i2i2i−2i−2i2i2i000000000000-1-111iii−i−i−iiii−i−i−i0000000000000000000000−i3i3−i3i3−33−330000
χ34222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-122-1-1-1−2i2i−2i2i11-2-2111111−2i−2i2i2i−2i−2i2i2i000000000000-1-111iii−i−i−iiii−i−i−i0000000000000000000000i3−i3i3−i33−33−30000
χ352222-2-2222-22-222222222222-2-2-2-222200002-2-2-222222-200000000222222222222-2-2-2-200000000000000000000-2-20000-2-2-2-20000000000000000
χ362222-2-2222-22-222222222222-2-2-2-222200002-2-2-222222-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000022220000000000000000
χ372222-2-222-22-22222222-2-2-2-22-2-2-2-22220000-2222-2-2-2-2-2200000000000000000000-2-22200000000000022-2-2222200-2-2-2-200000000000000000000
χ382222-2-222-22-22222222-2-2-2-22-2-2-2-22220000-2222-2-2-2-2-2200000000000000000000-2-222000000000000-2-222-2-2-2-200222200000000000000000000
χ392222-2-22-12-22-22-1-12-12-1-1-1-1-1-2-211-1-1-100002-211-1-12-1-1-2−i3i3−i3i3−i3i3−i3i32222-1-1-1-1-1-1-1-111110−i3i30−i3i30−i3i30−i3i30000−i3i3−i3i3-2-2i3−i3i3−i311110000000000000000
χ402222-2-22-12-22-22-1-12-12-1-1-1-1-1-2-211-1-1-100002-211-1-12-1-1-2−i3i3−i3i3−i3i3−i3i3-2-2-2-21111111111110−i3i30−i3i30−i3i30−i3i30000i3−i3i3−i322−i3i3−i3i3-1-1-1-10000000000000000
χ412222-2-22-12-22-22-1-12-12-1-1-1-1-1-2-211-1-1-100002-211-1-12-1-1-2i3−i3i3−i3i3−i3i3−i32222-1-1-1-1-1-1-1-111110i3−i30i3−i30i3−i30i3−i30000i3−i3i3−i3-2-2−i3i3−i3i311110000000000000000
χ422222-2-22-12-22-22-1-12-12-1-1-1-1-1-2-211-1-1-100002-211-1-12-1-1-2i3−i3i3−i3i3−i3i3−i3-2-2-2-21111111111110i3−i30i3−i30i3−i30i3−i30000−i3i3−i3i322i3−i3i3−i3-1-1-1-10000000000000000
χ432222-2-22-1-22-222-1-12-121111-1-2-211-1-1-10000-22-1-111-21123−3−333−3−33000033−3−333−3−311-1-103−30−3303−30−3322-2-2-1-1-1-1001111−33−330000000000000000
χ442222-2-22-1-22-222-1-12-121111-1-2-211-1-1-10000-22-1-111-21123−3−333−3−330000−3−333−3−33311-1-103−30−3303−30−33-2-222111100-1-1-1-13−33−30000000000000000
χ452222-2-22-1-22-222-1-12-121111-1-2-211-1-1-10000-22-1-111-2112−333−3−333−3000033−3−333−3−311-1-10−3303−30−3303−3-2-222111100-1-1-1-1−33−330000000000000000
χ462222-2-22-1-22-222-1-12-121111-1-2-211-1-1-10000-22-1-111-2112−333−3−333−30000−3−333−3−33311-1-10−3303−30−3303−322-2-2-1-1-1-10011113−33−30000000000000000
χ472-22-22-222-2-222-2-2-222-2-2-22222-22-2-2-222-2-22-22-22-2-2222-222-2-2-2-2220000000000002-2-22222-2-2-2-2-2-22220000000000000000000000000000000000
χ482-22-22-222-2-222-2-2-222-2-2-22222-22-2-2-22-222-2-22-22-2-2222-2-2-22222-2-20000000000002-2-22-2-2-2222222-2-2-20000000000000000000000000000000000
χ492-22-22-22-122-2-2-2112-1-2-1-111-12-2-1111-12i2i−2i−2i2-2-11-1-1-2112−i−i−i−iiiii2i2i−2i−2i−i−i−i−iiiii-11-112i−i−i2i−i−i−2iii−2iii2-22-2-1-1112i−2i-1-111−i−iii0000000000000000
χ502-22-22-22-122-2-2-2112-1-2-1-111-12-2-1111-12i2i−2i−2i2-2-11-1-1-2112−i−i−i−iiiii−2i−2i2i2iiiii−i−i−i−i-11-112i−i−i2i−i−i−2iii−2iii-22-2211-1-1−2i2i11-1-1ii−i−i0000000000000000
χ512-22-22-22-122-2-2-2112-1-2-1-111-12-2-1111-1−2i−2i2i2i2-2-11-1-1-2112iiii−i−i−i−i2i2i−2i−2i−i−i−i−iiiii-11-11−2iii−2iii2i−i−i2i−i−i-22-2211-1-12i−2i11-1-1−i−iii0000000000000000
χ522-22-22-22-122-2-2-2112-1-2-1-111-12-2-1111-1−2i−2i2i2i2-2-11-1-1-2112iiii−i−i−i−i−2i−2i2i2iiiii−i−i−i−i-11-11−2iii−2iii2i−i−i2i−i−i2-22-2-1-111−2i2i-1-111ii−i−i0000000000000000
χ532-22-22-22-1-2-222-2112-1-211-1-1-12-2-1111-12-2-22-221-1112-1-1-2-1-11111-1-10000−i3−i3i3i3i3i3−i3−i3-111-12-1-1-211-2112-1-10000−i3i3i3−i300−i3i3i3−i3−i3i3i3−i30000000000000000
χ542-22-22-22-1-2-222-2112-1-211-1-1-12-2-1111-12-2-22-221-1112-1-1-2-1-11111-1-10000i3i3−i3−i3−i3−i3i3i3-111-12-1-1-211-2112-1-10000i3−i3−i3i300i3−i3−i3i3i3−i3−i3i30000000000000000
χ552-22-22-22-1-2-222-2112-1-211-1-1-12-2-1111-1-222-2-221-1112-1-1-211-1-1-1-1110000−i3−i3i3i3i3i3−i3−i3-111-1-2112-1-12-1-1-2110000i3−i3−i3i300i3−i3−i3i3−i3i3i3−i30000000000000000
χ562-22-22-22-1-2-222-2112-1-211-1-1-12-2-1111-1-222-2-221-1112-1-1-211-1-1-1-1110000i3i3−i3−i3−i3−i3i3i3-111-1-2112-1-12-1-1-2110000−i3i3i3−i300−i3i3i3−i3i3−i3−i3i30000000000000000
χ572-22-22-2-1222-2-21-2-2-12122-2-2-1-112-211-12i2i−2i−2i-112-2-1-1111-12i2i2i2i−2i−2i−2i−2i000000000000-11-11−i−i−i−i−i−iiiiiii0000000000000000002i−2i2-2−i−iii-1-1110000
χ582-22-22-2-1222-2-21-2-2-12122-2-2-1-112-211-12i2i−2i−2i-112-2-1-1111-12i2i2i2i−2i−2i−2i−2i000000000000-11-11−i−i−i−i−i−iiiiiii000000000000000000−2i2i-22ii−i−i11-1-10000
χ592-22-22-2-1222-2-21-2-2-12122-2-2-1-112-211-1−2i−2i2i2i-112-2-1-1111-1−2i−2i−2i−2i2i2i2i2i000000000000-11-11iiiiii−i−i−i−i−i−i0000000000000000002i−2i-22−i−iii11-1-10000
χ602-22-22-2-1222-2-21-2-2-12122-2-2-1-112-211-1−2i−2i2i2i-112-2-1-1111-1−2i−2i−2i−2i2i2i2i2i000000000000-11-11iiiiii−i−i−i−i−i−i000000000000000000−2i2i2-2ii−i−i-1-1110000
χ612-22-22-2-12-2-2221-2-2-121-2-222-1-112-211-12-2-221-1-2211-1-1-1122-2-2-2-222000000000000-111-1-1-1-1111111-1-1-100000000000000000000003−3−33−333−30000
χ622-22-22-2-12-2-2221-2-2-121-2-222-1-112-211-12-2-221-1-2211-1-1-1122-2-2-2-222000000000000-111-1-1-1-1111111-1-1-10000000000000000000000−333−33−3−330000
χ632-22-22-2-12-2-2221-2-2-121-2-222-1-112-211-1-222-21-1-2211-1-1-11-2-22222-2-2000000000000-111-1111-1-1-1-1-1-111100000000000000000000003−3−333−3−330000
χ642-22-22-2-12-2-2221-2-2-121-2-222-1-112-211-1-222-21-1-2211-1-1-11-2-22222-2-2000000000000-111-1111-1-1-1-1-1-11110000000000000000000000−333−3−333−30000
χ652-22-2-22222-2-22-2-2-222-222-2-22-22-22-2-22000022-2222-2-2-2-2000000002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-22-2200000000000000000000−2i2i0000−2i−2i2i2i0000000000000000
χ662-22-2-22222-2-22-2-2-222-222-2-22-22-22-2-22000022-2222-2-2-2-200000000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-22-22000000000000000000002i−2i00002i2i−2i−2i0000000000000000
χ672-22-2-2222-222-2-2-2-222-2-2-2222-22-22-2-220000-2-22-2-2-2222200000000000000000000-222-20000000000002-2-2222-2-200-2-22200000000000000000000
χ682-22-2-2222-222-2-2-2-222-2-2-2222-22-22-2-220000-2-22-2-2-2222200000000000000000000-222-2000000000000-222-2-2-2220022-2-200000000000000000000
χ692-22-2-222-12-2-22-2112-1-2-1-111-1-221-111-10000221-1-1-1-211-23−33−3−33−332i2i−2i−2i−i−i−i−iiiii1-11-103−303−30−330−330000−i3i3i3−i3−2i2ii3−i3−i3i3ii−i−i0000000000000000
χ702-22-2-222-12-2-22-2112-1-2-1-111-1-221-111-10000221-1-1-1-211-23−33−3−33−33−2i−2i2i2iiiii−i−i−i−i1-11-103−303−30−330−330000i3−i3−i3i32i−2i−i3i3i3−i3−i−iii0000000000000000
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χ854444-4-4-2-2-44-44-2-2-2-2-2-222221222211100002-2-2-2-1-12-1-1-223−23−232323−23−2323000000000000-1-1110−3303−30−3303−30000000000000000000000000000000000
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χ8944-4-4004-200004-22-42-423−2323−23-20000-2220000000023−23023−23000000000−2i22i2−2i22i22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000000000
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χ944-44-44-4-2-244-4-4222-2-22-2-2221-22-22-1-11−4i−4i4i4i-22-22112-1-1-22i2i2i2i−2i−2i−2i−2i0000000000001-11-12i−i−i2i−i−i−2iii−2iii0000000000000000000000000000000000
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χ1014-44-4-44-2-2-444-4222-2-2222-2-212-22-2-1-11000022-22-1-1-211-2−2i32i32i3−2i32i3−2i3−2i32i3000000000000-111-10i3−i30−i3i30−i3i30i3−i30000000000000000000000000000000000
χ1024-44-4-44-2-2-444-4222-2-2222-2-212-22-2-1-11000022-22-1-1-211-22i3−2i3−2i32i3−2i32i32i3−2i3000000000000-111-10−i3i30i3−i30i3−i30−i3i30000000000000000000000000000000000
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χ1074-4-44004-20000-42-2-424−232323−23-200002-2200000000−2323023−2300000000022−22−22222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000000000
χ1084-4-44004-20000-42-2-424−232323−23-200002-2200000000−2323023−23000000000−222222−22−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000000000
χ10988-8-800-480000-48-84-840000-40000-444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-800-4-40000-4-4444443−4343−43200002-2-200000000−23230−232300000000000000000000000000000000000000000000000000000000000000000000000
χ11188-8-800-4-40000-4-44444−4343−4343200002-2-20000000023−23023−2300000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-8800-4800004-884-8-40000-400004-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-8800-4-4000044-444-443−43−434320000-22-200000000−2323023−2300000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-8800-4-4000044-444-4−434343−4320000-22-20000000023−230−232300000000000000000000000000000000000000000000000000000000000000000000000

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