Finite Group Databasebeta

← Group #13161377

Character table — Group #13161377

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122222222222222244444444444444444444444444444444444488888888888888888888888888888888181818181818242424242424242424242424242424242424363636363636363636216216
order1223333344666661212233334666666666661212121212121212121212121212121212121266666666666666661212121212121212121212121212121288242424242666666668242424242424242488824242424242428
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-11111-11-1-11111111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1
χ611111111111111111-11111-11-1-11111111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-11
χ711111111111111111-11111-11-1-11111111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-11
χ811111111111111111-11111-11-1-11111111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-111111-1
χ922222222-2-222222-2-202222020022222222-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000-2-2-2-20000000000000000000000000000000002i−2i002i2i−2i−2i00
χ1022222222-2-222222-2-202222020022222222-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000-2-2-2-2000000000000000000000000000000000−2i2i00−2i−2i2i2i00
χ1122222-1-1-12222-1-1-12222-1-1-122222-1-1-12-1-1-122-1-1-12222-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000000222-1-1-1-1-1-1222-1-1-1-1-1-100000000000
χ1222222-1-1-12222-1-1-12222-1-1-122222-1-1-12-1-1-122-1-1-12222-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000000-2-2-2111111-2-2-211111100000000000
χ1322222-1-1-12222-1-1-122-22-1-1-1-22-2-22-1-1-12-1-1-122-1-1-1-2-222-1-1-1-1-1-12-1-1-1-21112-1-1-1-2-2111111-21112-1-1-1-2-2111111000000222-1-1-1-1-1-1-2-2-211111100000000000
χ1422222-1-1-12222-1-1-122-22-1-1-1-22-2-22-1-1-12-1-1-122-1-1-1-2-222-1-1-1-1-1-12-1-1-1-21112-1-1-1-2-2111111-21112-1-1-1-2-2111111000000-2-2-2111111222-1-1-1-1-1-100000000000
χ152222-12-1-1222-12-1-1222-12-1-12222-12-1-1-12-1-12-12-1-122-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-10000002-1-122-1-1-1-12-1-122-1-1-1-100000000000
χ162222-12-1-1222-12-1-1222-12-1-12222-12-1-1-12-1-12-12-1-122-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1000000-211-2-21111-211-2-2111100000000000
χ172222-12-1-1222-12-1-122-2-12-1-1-22-2-2-12-1-1-12-1-12-12-1-1-2-2-1-122-1-1-1-1-12-1-11-211-12-1-111-2-211111-211-12-1-111-2-211110000002-1-122-1-1-1-1-211-2-2111100000000000
χ182222-12-1-1222-12-1-122-2-12-1-1-22-2-2-12-1-1-12-1-12-12-1-1-2-2-1-122-1-1-1-1-12-1-11-211-12-1-111-2-211111-211-12-1-111-2-21111000000-211-2-211112-1-122-1-1-1-100000000000
χ192222-1-12-1222-1-12-1222-1-12-12222-1-12-1-1-12-12-1-12-122-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-10000002-1-1-1-122-1-12-1-1-1-122-1-100000000000
χ202222-1-12-1222-1-12-1222-1-12-12222-1-12-1-1-12-12-1-12-122-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1000000-21111-2-211-21111-2-21100000000000
χ212222-1-12-1222-1-12-122-2-1-12-1-22-2-2-1-12-1-1-12-12-1-12-1-2-2-1-1-1-122-1-1-1-12-111-21-1-12-11111-2-21111-21-1-12-11111-2-2110000002-1-1-1-122-1-1-21111-2-21100000000000
χ222222-1-12-1222-1-12-122-2-1-12-1-22-2-2-1-12-1-1-12-12-1-12-1-2-2-1-1-1-122-1-1-1-12-111-21-1-12-11111-2-21111-21-1-12-11111-2-211000000-21111-2-2112-1-1-1-122-1-100000000000
χ232222-1-1-12222-1-1-12222-1-1-122222-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-1220000002-1-1-1-1-1-1222-1-1-1-1-1-12200000000000
χ242222-1-1-12222-1-1-12222-1-1-122222-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122000000-2111111-2-2-2111111-2-200000000000
χ252222-1-1-12222-1-1-1222-2-1-1-12-22-2-2-1-1-12-1-1-122-1-1-12-2-2-1-1-1-1-1-122-1-1-12111-2-1-1-12111111-2-2111-2-1-1-12111111-2-20000002-1-1-1-1-1-122-2111111-2-200000000000
χ262222-1-1-12222-1-1-1222-2-1-1-12-22-2-2-1-1-12-1-1-122-1-1-12-2-2-1-1-1-1-1-122-1-1-12111-2-1-1-12111111-2-2111-2-1-1-12111111-2-2000000-2111111-2-22-1-1-1-1-1-12200000000000
χ27222-1222222-12222-1-12-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000000000222-1-1-1-1-1-100
χ28222-1222222-12222-1-12-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000000000000000-2-2-211111100
χ29222-1222222-12222-1-1-2-1-1-1-1-2-1112222-1-1-1-1-1222211-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-1-11111111122-1-1-1-10000000000000000002-2-2-1-1111100
χ30222-1222222-12222-1-1-2-1-1-1-1-2-1112222-1-1-1-1-1222211-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-1-111111111-2-21111000000000000000000-22211-1-1-1-100
χ31222-12222-2-2-12222110-1-1-1-10-1−i3i32222-1-1-1-11-2-2-2-2−i3i311111111-2-2-2-20000-1-1-1-1−i3i3−i3i3−i3i3−i3i300001111−i3i3−i3i3−i3i3−i3i30033−3−300000000000000000002i−2i3−3−i−iii00
χ32222-12222-2-2-12222110-1-1-1-10-1−i3i32222-1-1-1-11-2-2-2-2−i3i311111111-2-2-2-20000-1-1-1-1−i3i3−i3i3−i3i3−i3i300001111−i3i3−i3i3−i3i3−i3i300−3−3330000000000000000000−2i2i−33ii−i−i00
χ33222-12222-2-2-12222110-1-1-1-10-1i3−i32222-1-1-1-11-2-2-2-2i3−i311111111-2-2-2-20000-1-1-1-1i3−i3i3−i3i3−i3i3−i300001111i3−i3i3−i3i3−i3i3−i30033−3−30000000000000000000−2i2i3−3ii−i−i00
χ34222-12222-2-2-12222110-1-1-1-10-1i3−i32222-1-1-1-11-2-2-2-2i3−i311111111-2-2-2-20000-1-1-1-1i3−i3i3−i3i3−i3i3−i300001111i3−i3i3−i3i3−i3i3−i300−3−33300000000000000000002i−2i−33−i−iii00
χ3522-2222222-22222222022220-200-2-2-2-22222-222220022222222-2-2-2-20000-2-2-2-2000000000000-2-2-2-200000000222222000000000000000000-200-2-2000000
χ3622-2222222-22222222022220-200-2-2-2-22222-222220022222222-2-2-2-20000-2-2-2-2000000000000-2-2-2-200000000-2-2-2-2-2-200000000000000000020022000000
χ3722-222222-2222222-2-222222-2-222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000
χ3822-222222-2222222-2-2-222222-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222200000000000000000000000000000000000
χ3922-222-1-1-1-2222-1-1-1-2-222-1-1-1-2-222-21112-1-1-12-2111-2-2-2-21111112-1-1-12-1-1-1-211122-1-1-1-1-1-1-21112-1-1-1-2-2111111000000000−i3i3−i3i3−i3i3000−i3i3−i3i3−i3i300000000000
χ4022-222-1-1-1-2222-1-1-1-2-222-1-1-1-2-222-21112-1-1-12-2111-2-2-2-21111112-1-1-12-1-1-1-211122-1-1-1-1-1-1-21112-1-1-1-2-2111111000000000i3−i3i3−i3i3−i3000i3−i3i3−i3i3−i300000000000
χ4122-222-1-1-1-2222-1-1-1-2-2-22-1-1-12-2-2-2-21112-1-1-12-211122-2-21111112-1-1-1-2111-2111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1000000000−i3i3−i3i3−i3i3000i3−i3i3−i3i3−i300000000000
χ4222-222-1-1-1-2222-1-1-1-2-2-22-1-1-12-2-2-2-21112-1-1-12-211122-2-21111112-1-1-1-2111-2111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1000000000i3−i3i3−i3i3−i3000−i3i3−i3i3−i3i300000000000
χ4322-22-12-1-1-222-12-1-1-2-22-12-1-1-2-2221-211-12-1-121-211-2-211-2-21111-12-1-1-12-1-11-211-1-122-1-1-1-11-211-12-1-111-2-211110000000−i3i300−i3i3i3−i30−i3i300−i3i3i3−i300000000000
χ4422-22-12-1-1-222-12-1-1-2-22-12-1-1-2-2221-211-12-1-121-211-2-211-2-21111-12-1-1-12-1-11-211-1-122-1-1-1-11-211-12-1-111-2-211110000000i3−i300i3−i3−i3i30i3−i300i3−i3−i3i300000000000
χ4522-22-12-1-1-222-12-1-1-2-2-2-12-1-12-2-2-21-211-12-1-121-2112211-2-21111-12-1-11-2111-21111-2-21111-12-1-1-12-1-1-1-122-1-1-1-10000000−i3i300−i3i3i3−i30i3−i300i3−i3−i3i300000000000
χ4622-22-12-1-1-222-12-1-1-2-2-2-12-1-12-2-2-21-211-12-1-121-2112211-2-21111-12-1-11-2111-21111-2-21111-12-1-1-12-1-1-1-122-1-1-1-10000000i3−i300i3−i3−i3i30−i3i300−i3i3i3−i300000000000
χ4722-22-1-12-1-222-1-12-1-2-22-1-12-1-2-22211-21-1-12-1211-21-2-21111-2-211-1-12-1-1-12-111-21-1-1-1-122-1-111-21-1-12-11111-2-2110000000−i3i3i3−i300−i3i30−i3i3i3−i300−i3i300000000000
χ4822-22-1-12-1-222-1-12-1-2-22-1-12-1-2-22211-21-1-12-1211-21-2-21111-2-211-1-12-1-1-12-111-21-1-1-1-122-1-111-21-1-12-11111-2-2110000000i3−i3−i3i300i3−i30i3−i3−i3i300i3−i300000000000
χ4922-22-1-12-1-222-1-12-1-2-2-2-1-12-12-2-2-211-21-1-12-1211-21221111-2-211-1-12-111-2111-211111-2-211-1-12-1-1-12-1-1-1-1-122-1-10000000−i3i3i3−i300−i3i30i3−i3−i3i300i3−i300000000000
χ5022-22-1-12-1-222-1-12-1-2-2-2-1-12-12-2-2-211-21-1-12-1211-21221111-2-211-1-12-111-2111-211111-2-211-1-12-1-1-12-1-1-1-1-122-1-10000000i3−i3−i3i300i3−i30−i3i3i3−i300−i3i300000000000
χ5122-22-1-1-12-222-1-1-12-2-22-1-1-12-2-222111-2-1-1-122111-2-2-2111111-2-2-1-1-12-1-1-12111-2-1-1-1-1-1-122111-2-1-1-12111111-2-20000000−i3i3−i3i3i3−i3000−i3i3−i3i3i3−i30000000000000
χ5222-22-1-1-12-222-1-1-12-2-22-1-1-12-2-222111-2-1-1-122111-2-2-2111111-2-2-1-1-12-1-1-12111-2-1-1-1-1-1-122111-2-1-1-12111111-2-20000000i3−i3i3−i3−i3i3000i3−i3i3−i3−i3i30000000000000
χ5322-22-1-1-12-222-1-1-12-2-2-2-1-1-122-2-2-2111-2-1-1-122111-222111111-2-2-1-1-12111-2111-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-1220000000−i3i3−i3i3i3−i3000i3−i3i3−i3−i3i30000000000000
χ5422-22-1-1-12-222-1-1-12-2-2-2-1-1-122-2-2-2111-2-1-1-122111-222111111-2-2-1-1-12111-2111-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-1220000000i3−i3i3−i3−i3i3000−i3i3−i3i3i3−i30000000000000
χ5522-2-122222-2-12222-1-10-1-1-1-101−i3i3-2-2-2-2-1-1-1-112222i3−i3-1-1-1-1-1-1-1-1-2-2-2-200001111−i3i3−i3i3−i3i3−i3i300001111i3−i3i3−i3i3−i3i3−i322-1-1-1-1000000000000000000-20011−i3i3−i3i300
χ5622-2-122222-2-12222-1-10-1-1-1-101−i3i3-2-2-2-2-1-1-1-112222i3−i3-1-1-1-1-1-1-1-1-2-2-2-200001111−i3i3−i3i3−i3i3−i3i300001111i3−i3i3−i3i3−i3i3−i3-2-21111000000000000000000200-1-1i3−i3i3−i300
χ5722-2-122222-2-12222-1-10-1-1-1-101i3−i3-2-2-2-2-1-1-1-112222−i3i3-1-1-1-1-1-1-1-1-2-2-2-200001111i3−i3i3−i3i3−i3i3−i300001111−i3i3−i3i3−i3i3−i3i322-1-1-1-1000000000000000000-20011i3−i3i3−i300
χ5822-2-122222-2-12222-1-10-1-1-1-101i3−i3-2-2-2-2-1-1-1-112222−i3i3-1-1-1-1-1-1-1-1-2-2-2-200001111i3−i3i3−i3i3−i3i3−i300001111−i3i3−i3i3−i3i3−i3i3-2-21111000000000000000000200-1-1−i3i3−i3i300
χ5922-2-12222-22-12222112-1-1-1-1-21-1-1-2-2-2-2-1-1-1-1-1-2-2-2-21111111111222222221111-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1111111110033−3−3000000000000000000000−333−3−3300
χ6022-2-12222-22-12222112-1-1-1-1-21-1-1-2-2-2-2-1-1-1-1-1-2-2-2-21111111111222222221111-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111100−3−3330000000000000000000003−3−333−300
χ6122-2-12222-22-1222211-2-1-1-1-12111-2-2-2-2-1-1-1-1-1-2-2-2-2-1-1111111112222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-10033−3−3000000000000000000000−33−333−300
χ6222-2-12222-22-1222211-2-1-1-1-12111-2-2-2-2-1-1-1-1-1-2-2-2-2-1-1111111112222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100−3−3330000000000000000000003−33−3−3300
χ6344444-2-2-2-4-444-2-2-2-4-404-2-2-204004-2-2-24-2-2-2-4-422200-4-4222222-422200004-2-2-2000000000000-42220000000000000000000000000000000000000000000
χ644444-24-2-2-4-44-24-2-2-4-40-24-2-20400-24-2-2-24-2-2-42-4220022-4-422222-4220000-24-2-20000000000002-4220000000000000000000000000000000000000000000
χ654444-2-24-2-4-44-2-24-2-4-40-2-24-20400-2-24-2-2-24-2-422-42002222-4-42222-420000-2-24-200000000000022-420000000000000000000000000000000000000000000
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χ1054-40-24444002-4-4-4-423−230-2-2-2-2000000002222000000023−2323−2323−2323−2300000000000000000000000000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.