Finite Group Databasebeta

← Group #11772444

Character table — Group #11772444

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11112222222222222222222222222244444444444444444444444444444444444444444444444444444444442424242424242424242424242424242424242424242424243636363636363636
order1244222334446666668888121212121212121236666666666688121212121212121212121212242424242424242424242424242424242424242424242424242424242424242444444444121212121212121212121212121212121616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-111-1-1111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ611111-1-111-1-1111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ711111-1-111-1-1111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ811111-1-111-1-1111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ911-1-1-11-1111-111111-1-111-1-1-1-1-1-111-1-11-1-11-1-1-111-1-111-11-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-1-11-1111-111111-1-111-1-1-1-1-1-111-1-11-1-11-1-1-111-1-111-11-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-1-11-1111-111111-1-111-1-1-1-1-1-111-1-11-1-11-1-1-111-1-111-11-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-1-11-1111-111111-1-111-1-1-1-1-1-111-1-11-1-11-1-1-111-1-111-11-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-1-1111-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1111-11-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ1411-1-1-1-1111-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1111-11-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ1511-1-1-1-1111-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1111-11-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ1611-1-1-1-1111-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1111-11-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−iii−i-111-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ17222222222222222222-2-2-2-222222222222222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222-12222-122-1-1222222-1-1-1-122-12-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ1922222222-12222-122-1-1222222-1-1-1-122-12-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ2022222222-12222-122-1-1-2-2-2-222-1-1-1-122-12-1-12-1-1-1-1-1-1-1-2-22-1-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-21111110000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2122222222-12222-122-1-1-2-2-2-222-1-1-1-122-12-1-12-1-1-1-1-1-1-1-2-22-1-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111-2-2111111-2-21111110000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ222222222-12222-12-1-1222222-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ232222222-12222-12-1-1222222-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-20000111111110000000000000000
χ242222222-12222-12-1-122-2-2-2-2-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-12-1-1-1-1-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-2111100000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ252222222-12222-12-1-122-2-2-2-2-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-12-1-1-1-1-1-1-12-1-111-2-2111111-2-2111111-2-2111111-2-2111100000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2622222-2-222-2-2222-2-2-2-2-2-2-2-22222-2-2-2-2222-2-222-2-2-2-2222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222200000000000000000000000000000000
χ2722222-2-22-1-2-222-1-2-211222222-1-111-2-2-12-11-2-1-11111-1-2-2-21-1-111112-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-211111100002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ2822222-2-22-1-2-222-1-2-211222222-1-111-2-2-12-11-2-1-11111-1-2-2-21-1-111112-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-21111110000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ2922222-2-22-1-2-222-1-2-211-2-2-2-222-1-111-2-2-12-11-2-1-11111-122-21-1-111112-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-100000000000000003−33−3−33−3300000000
χ3022222-2-22-1-2-222-1-2-211-2-2-2-222-1-111-2-2-12-11-2-1-11111-122-21-1-111112-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000−33−333−33−300000000
χ3122222-2-2-12-2-22-1211-2-22222-1-122-2-211-1-12-21-1-11111-1-2-21-2-1-11111-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-211112i2i−2i−2i0000−i−i−i−iiiii0000000000000000
χ3222222-2-2-12-2-22-1211-2-22222-1-122-2-211-1-12-21-1-11111-1-2-21-2-1-11111-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111−2i−2i2i2i0000iiii−i−i−i−i0000000000000000
χ3322222-2-2-12-2-22-1211-2-2-2-2-2-2-1-122-2-211-1-12-21-1-11111-1221-2-1-11111-12-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-1000000003−33−3−33−330000000000000000
χ3422222-2-2-12-2-22-1211-2-2-2-2-2-2-1-122-2-211-1-12-21-1-11111-1221-2-1-11111-12-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-100000000−33−333−33−30000000000000000
χ352222-22-222-22-22222-2-200002222-2-2222-2-22-2-2-222-2-2200-2222-2-222-2-2-2-200000000000000000000000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ362222-22-222-22-22222-2-200002222-2-2222-2-22-2-2-222-2-2200-2222-2-222-2-2-2-200000000000000000000000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ372222-2-22222-2-222-2-2220000222222-2-22-2-2-22-2-2-2-2222002-22222-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ382222-2-22222-2-222-2-2220000222222-2-22-2-2-22-2-2-2-2222002-22222-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ3922-2-222222-2-2-22222220000-2-2-2-2-2-2-2-222222222222200-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000000000002−2−222−2−22
χ4022-2-222222-2-2-22222220000-2-2-2-2-2-2-2-222222222222200-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000−222−2−222−2
χ4122-2-22-2-22222-222-2-2-2-20000-2-2-2-22222222-2-222-2-2-2-220022-2-22222-2-2-2-2000000000000000000000000000000000000000000000000000000002−2−22−222−2
χ4222-2-22-2-22222-222-2-2-2-20000-2-2-2-22222222-2-222-2-2-2-220022-2-22222-2-2-2-200000000000000000000000000000000000000000000000000000000−222−22−2−22
χ4322-2-2-22-2222-222222-2-2-2-222-2-2-2-222-2-22-2-22-2-2-222-2-22-222-2-2-222-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ4422-2-2-22-22-12-222-1221122-2-2-2-211-1-1-2-2-1-21-1-211-1-111-12-22111-1-1112-1-1-122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-211111100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ4522-2-2-22-22-12-222-1221122-2-2-2-211-1-1-2-2-1-21-1-211-1-111-12-22111-1-1112-1-1-122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-21111110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ4622-2-2-22-22-12-222-12211-2-222-2-211-1-1-2-2-1-21-1-211-1-111-1-222111-1-1112-1-1-1-2-211111122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-100000000000000003−3−333−3−3300000000
χ4722-2-2-22-22-12-222-12211-2-222-2-211-1-1-2-2-1-21-1-211-1-111-1-222111-1-1112-1-1-1-2-211111122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-10000000000000000−333−3−333−300000000
χ4822-2-2-22-2-122-22-12-1-1-2-222-2-211-2-22211-11-22111-1-111-12-2-1-211-1-111-12-1-1-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-211112-22-20000-1-111-1-1110000000000000000
χ4922-2-2-22-2-122-22-12-1-1-2-222-2-211-2-22211-11-22111-1-111-12-2-1-211-1-111-12-1-1-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-21111-22-22000011-1-111-1-10000000000000000
χ5022-2-2-22-2-122-22-12-1-1-2-2-2-22211-2-22211-11-22111-1-111-1-22-1-211-1-111-12-1-111-2-21111-1-122-1-1-1-111-2-21111-1-122-1-1-1-100000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ5122-2-2-22-2-122-22-12-1-1-2-2-2-22211-2-22211-11-22111-1-111-1-22-1-211-1-111-12-1-111-2-21111-1-122-1-1-1-111-2-21111-1-122-1-1-1-100000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ5222-2-2-2-2222-22222-2-222-2-222-2-2-2-2-2-2222-2-2-22-2-2-2-22222-2-22-2-2-2-2222222-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ5322-2-2-2-222-1-2222-1-2-2-1-122-2-2-2-2111122-1-21121111-1-1-1-22-2-11111-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-100002-2-2200000000-1-11111-1-100000000
χ5422-2-2-2-222-1-2222-1-2-2-1-122-2-2-2-2111122-1-21121111-1-1-1-22-2-11111-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-10000-222-20000000011-1-1-1-11100000000
χ5522-2-2-2-222-1-2222-1-2-2-1-1-2-222-2-2111122-1-21121111-1-1-12-2-2-11111-1-12-1-1-1-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1-2-21111110000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ5622-2-2-2-222-1-2222-1-2-2-1-1-2-222-2-2111122-1-21121111-1-1-12-2-2-11111-1-12-1-1-1-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1-2-21111110000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ5722-2-2-2-22-12-222-12112222-2-211-2-2-2-2-1-1-11-2-2-11111-1-1-1-22121111-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ5822-2-2-2-22-12-222-12112222-2-211-2-2-2-2-1-1-11-2-2-11111-1-1-1-22121111-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ5922-2-2-2-22-12-222-121122-2-22211-2-2-2-2-1-1-11-2-2-11111-1-1-12-2121111-1-1-12-1-111-2-21111-1-122-1-1-1-1-1-122-1-1-1-111-2-21111000000003−3−33−333−30000000000000000
χ6022-2-2-2-22-12-222-121122-2-22211-2-2-2-2-1-1-11-2-2-11111-1-1-12-2121111-1-1-12-1-111-2-21111-1-122-1-1-1-1-1-122-1-1-1-111-2-2111100000000−333−33−3−330000000000000000
χ614444444-2-2444-2-2-2-2-2-24444-2-2-2-2-2-2-2-21-2-2-2-2111111144-2-2111111-2-211-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-2111100000000000000000000000000000000
χ624444444-2-2444-2-2-2-2-2-2-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-21111111-4-4-2-2111111-2-2112222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ6344444-4-4-2-2-4-44-2-222224444-2-2-2-222221-2-22211-1-1-1-11-4-42211-1-1-1-1-2-211-2-2-2-21111-2-2-2-211112222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ6444444-4-4-2-2-4-44-2-22222-4-4-4-4-2-2-2-222221-2-22211-1-1-1-11442211-1-1-1-1-2-2112222-1-1-1-12222-1-1-1-1-2-2-2-21111-2-2-2-2111100000000000000000000000000000000
χ654444-44-44-2-44-44-24422000044-2-22244-2-42-2-422-2-222-200-4-2-2-222-2-2-42220000000000000000000000000000000000000000000000000000000000000000
χ664444-44-4-24-44-4-24-2-2-4-40000-2-244-4-4-2-2-22-44222-2-222-20024-2-222-2-22-4220000000000000000000000000000000000000000000000000000000000000000
χ674444-44-4-2-2-44-4-2-2-2-2220000-2-2-2-222-2-2122-22-1-111-1-11002-211-1-11122-1-100003i3i−3i−3i00003i3i−3i−3i00003i3i−3i−3i00003i3i−3i−3i00000000000000000000000000000000
χ684444-44-4-2-2-44-4-2-2-2-2220000-2-2-2-222-2-2122-22-1-111-1-11002-211-1-11122-1-10000−3i−3i3i3i0000−3i−3i3i3i0000−3i−3i3i3i0000−3i−3i3i3i00000000000000000000000000000000
χ694444-4-444-24-4-44-2-4-4-2-2000044-2-2-2-2-4-4-2-42242222-2-2-20042-2-2-2-222-42220000000000000000000000000000000000000000000000000000000000000000
χ704444-4-44-244-4-4-2422440000-2-2444422-22-4-4-22222-2-2-200-2-4-2-2-2-2222-4220000000000000000000000000000000000000000000000000000000000000000
χ714444-4-44-2-24-4-4-2-222-2-20000-2-2-2-2-2-2221222-2-1-1-1-111100-221111-1-122-1-100003i3i−3i−3i00003i3i−3i−3i0000−3i−3i3i3i0000−3i−3i3i3i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.