Finite Group Databasebeta

← Group #13170599

Character table — Group #13170599

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11222222222222244444444444444444444444666666666688888888888812121212121212121212121212121212121212121212121212121212122424242424242424242436363636363636363636363636367272108108
order122333446661212121233366666666121212121212121212121212224488242424243666661212121212122466666681212121212122424242424242424242424242424666661212121212244488121212122424242461244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-111111-1-111111111111111-111-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1111-1-1-1-111111111111111111-1-1111-1-1111-1-11-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111-1-111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-11111-11-11111111-1-1-1-111-111-1-11-11-11-111-11-11-1-1-1-1-1111111-1-1-1-1-1-111-111-11-1-1-111-1-11-111-1-111-1-11-11-1
χ1011-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-11111-11-11111111-1-1-1-111-111-1-1-111-11-1-1-1-11-11-111-1-1111111-1-1-1-1-1-1-11-1-1-111-111-1-1111-1-1-11111-1-1-11-11
χ1111-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-11111-11-1-1-1-1-1-1-11-1-1-1-111-111-1-11-11-11-11111-11-1-1-111-1-1-1-1-1-111111111-111-11-1-1-1-11-11-1111-1-1-1-111-11-11
χ1211-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-11111-11-1-1-1-1-1-1-11-1-1-1-111-111-1-1-111-11-1-1-111-11-11111-1-1-1-1-1-1111111-11-1-1-111-1111-11-1-11-1-111-1-1111-11-1
χ1311-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-1111-11-111111111-1-1-1-111-111-1-11-1-11-1111-1-11-11-1-1-1-1111111-1-1-1-1-1-11-1111-1-11-1-11-11-1-11-1-111-1-1111-1-11
χ1411-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-1111-11-111111111-1-1-1-111-111-1-1-11-11-11-1-1-1-11-1111-1-1111111-1-1-1-1-1-1-1-11-1-11-1111-11-11-1111-1-1-1-111-111-1
χ1511-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-1111-11-11-1-1-1-1-1-11-1-1-1-111-111-1-11-1-11-11111-11-11-1-111-1-1-1-1-1-11111111-1111-1-11-1-1-1-1111-1-1-11111-1-1-111-1
χ1611-1111-11111-1-111111-1-1-1-1-1111-11-1-1-111-1-1111-11-11-1-1-1-1-1-11-1-1-1-111-111-1-1-11-11-11-1-11-11-111111-1-1-1-1-1-1111111-1-11-1-11-111111-1-11-111-1-111-1-11-1-11
χ17222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22000000222222-2-2-2-2-2-2002-22-2000-22-22000000000000000002-2000-2200000000000000000000
χ18222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2000000222222-2-2-2-2-2-200-22-220002-22-200000000000000000-220002-200000000000000000000
χ1922222-1222-12-1-122-12-122-1-1-1-12-1222-1-122-1-1-1-1-10000222222-12-1-1-1-1-12-1-1-1-122000022200002222-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1-100-1-120020000000000-1-100
χ2022222-1222-12-1-122-12-122-1-1-1-12-1222-1-122-1-1-1-1-10000222222-12-1-1-1-1-12-1-1-1-1-2-20000-2-220000-2-222-1-1-1-1-1-1-1-1-1-1-1-11001110011-200-200000000001100
χ2122222-1222-12-1-122-12-122-1-1-1-12-1222-1-122-1-1-1-1-10000-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-122000022-2000022-2-2111111111111-100-1-1-100-1-1-200-200000000001100
χ2222222-1222-12-1-122-12-122-1-1-1-12-1222-1-122-1-1-1-1-10000-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-1-2-20000-2-2-20000-2-2-2-2111111111111100111001120020000000000-1-100
χ232222-122222-122222-1-12-12222-1-12-1-122-1-1-1-12222222000000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1022-1-1-1-1000000000000002-1-1-1-12-1-1-1-1022000-1-1-1-100000000
χ242222-122222-122222-1-12-12222-1-12-1-122-1-1-1-12222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-222-1-111022-1-11100000000000000-2-1-111-2-1-1110-2-2000111100000000
χ252222-122222-122222-1-12-12222-1-12-1-122-1-1-1-1222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-122-2-211-1-10-2-211-1-100000000000000211-1-1211-1-10-2-2000111100000000
χ262222-122222-122222-1-12-12222-1-12-1-122-1-1-1-1222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110-2-2111100000000000000-21111-21111022000-1-1-1-100000000
χ272222-12-2-222-1-2-2-2-22-1-12-12222-1-1-211-2-21111-2-2-22-2-22000000-1-1-1-1-1-1111111002-2-11−i3i30-221-1−i3i3000000000000000-11−i3i301-1−i3i3000000−i3i3−i3i300000000
χ282222-12-2-222-1-2-2-2-22-1-12-12222-1-1-211-2-21111-2-2-22-2-22000000-1-1-1-1-1-1111111002-2-11i3−i30-221-1i3−i3000000000000000-11i3−i301-1i3−i3000000i3−i3i3−i300000000
χ292222-12-2-222-1-2-2-2-22-1-12-12222-1-1-211-2-21111-2-2-2-222-2000000-1-1-1-1-1-111111100-221-1−i3i302-2-11−i3i30000000000000001-1−i3i30-11−i3i3000000i3−i3i3−i300000000
χ302222-12-2-222-1-2-2-2-22-1-12-12222-1-1-211-2-21111-2-2-2-222-2000000-1-1-1-1-1-111111100-221-1i3−i302-2-11i3−i30000000000000001-1i3−i30-11i3−i3000000−i3i3−i3i300000000
χ31222-12222-12222-1-1-1-12-122-1-1-1-12-122-1-1-1-1222-1-1222222-1-1-1-1-1-12-1-1-12-1-1-1-1-100-1-122002-1-12200-1-122-1-1-1-122-1-1-1-10-1-1000-1-1000000220000-1-1-1-10000
χ32222-12222-12222-1-1-1-12-122-1-1-1-12-122-1-1-1-1222-1-12222-2-21111-1-12-1-1-12-1-1-1-1-100-1-12200-2-1-1220011-2-21111-2-211110-1-1000-1-1000000-2-2000011110000
χ33222-12222-12222-1-1-1-12-122-1-1-1-12-122-1-1-1-1222-1-1-2-2-2-222-1-1-1-1-1-12-1-1-12-1-1-1-1-10011-2-200211-2-200-1-122-1-1-1-122-1-1-1-101100011000000-2-2000011110000
χ34222-12222-12222-1-1-1-12-122-1-1-1-12-122-1-1-1-1222-1-1-2-2-2-2-2-21111-1-12-1-1-12-1-1-1-1-10011-2-200-211-2-20011-2-21111-2-2111101100011000000220000-1-1-1-10000
χ35222-122-2-2-122-2-211-1-12-122-1-1-1-121-2-21111-2-2-2112-2-220033−3−3-1-12-1-1-1-21111100-112-20001-1-22003−30033−3−30033−3−30-110001-10000000000003−33−30000
χ36222-122-2-2-122-2-211-1-12-122-1-1-1-121-2-21111-2-2-2112-2-2200−3−333-1-12-1-1-1-21111100-112-20001-1-2200−3300−3−33300−3−3330-110001-1000000000000−33−330000
χ37222-122-2-2-122-2-211-1-12-122-1-1-1-121-2-21111-2-2-211-222-20033−3−3-1-12-1-1-1-211111001-1-22000-112-2003−30033−3−30033−3−301-1000-11000000000000−33−330000
χ38222-122-2-2-122-2-211-1-12-122-1-1-1-121-2-21111-2-2-211-222-200−3−333-1-12-1-1-1-211111001-1-22000-112-200−3300−3−33300−3−33301-1000-110000000000003−33−30000
χ3922-22222-222222-2-2222-2-2-2-2-22222-2222-2-222-2-2-222-2-20000002-2-2-2-22-22-2-222002222000-2-2-2-20000000000000000022000-2-200000000000000000000
χ4022-22222-222222-2-2222-2-2-2-2-22222-2222-2-222-2-2-2-2-2220000002-2-2-2-22-22-2-22200-2-2-2-2000222200000000000000000-2-20002200000000000000000000
χ4122-222-1-222-121122-12-1-2-2111-12-1-22-2112211-1-1-10000222222-1-2111-1-1-2-1-1112-2000022-20000-2-2-2-2-1-1-1-1-1-1111111-100-1-110011200-20000000000-1100
χ4222-222-1-222-121122-12-1-2-2111-12-1-22-2112211-1-1-10000222222-1-2111-1-1-2-1-111-220000-2-2-2000022-2-2-1-1-1-1-1-111111110011-100-1-1-200200000000001-100
χ4322-222-1-222-121122-12-1-2-2111-12-1-22-2112211-1-1-10000-2-2-2-2-2-2-1-2111-1-1-2-1-1112-200002220000-2-222111111-1-1-1-1-1-1-100-1-110011-200200000000001-100
χ4422-222-1-222-121122-12-1-2-2111-12-1-22-2112211-1-1-10000-2-2-2-2-2-2-1-2111-1-1-2-1-111-220000-2-2200002222111111-1-1-1-1-1-110011-100-1-1200-20000000000-1100
χ4522-22-122-222-122-2-22-1-1-21-2-2-22-1-121-12211-1-1-2-2-222-2-2000000-11111-11-111-1-10022-1-1−i3i30-2-211i3−i3000000000000000-1-1−i3i3011i3−i3000000−i3i3i3−i300000000
χ4622-22-122-222-122-2-22-1-1-21-2-2-22-1-121-12211-1-1-2-2-222-2-2000000-11111-11-111-1-10022-1-1i3−i30-2-211−i3i3000000000000000-1-1i3−i3011−i3i3000000i3−i3−i3i300000000
χ4722-22-122-222-122-2-22-1-1-21-2-2-22-1-121-12211-1-1-2-2-2-2-222000000-11111-11-111-1-100-2-211−i3i3022-1-1i3−i300000000000000011−i3i30-1-1i3−i3000000i3−i3−i3i300000000
χ4822-22-122-222-122-2-22-1-1-21-2-2-22-1-121-12211-1-1-2-2-2-2-222000000-11111-11-111-1-100-2-211i3−i3022-1-1−i3i300000000000000011i3−i30-1-1−i3i3000000−i3i3i3−i300000000
χ4922-22-12-2222-1-2-2222-1-1-21-2-2-22-1-1-2-11-2-2-1-1112222-22-2000000-11111-1-11-1-1112-22-2-11-1-102-2-1111000000000000002-11-1-1-2-111102-2000-1-11100000000
χ5022-22-12-2222-1-2-2222-1-1-21-2-2-22-1-1-2-11-2-2-1-1112222-22-2000000-11111-1-11-1-111-222-2-111102-2-11-1-100000000000000-2-11112-11-1-10-2200011-1-100000000
χ5122-22-12-2222-1-2-2222-1-1-21-2-2-22-1-1-2-11-2-2-1-111222-22-22000000-11111-1-11-1-1112-2-221-1-1-10-221-1110000000000000021-1-1-1-21-1110-2200011-1-100000000
χ5222-22-12-2222-1-2-2222-1-1-21-2-2-22-1-1-2-11-2-2-1-111222-22-22000000-11111-1-11-1-111-22-221-1110-221-1-1-100000000000000-21-11121-1-1-102-2000-1-11100000000
χ5322-2-1222-2-1222211-1-121-2-211-1-12-1-22-1-11122-21122-2-20033−3−3-11-211-1-2-111-1-100-1-12200011-2-200−330033−3−300−3−3330-1-1000110000000000003−3−330000
χ5422-2-1222-2-1222211-1-121-2-211-1-12-1-22-1-11122-21122-2-200−3−333-11-211-1-2-111-1-100-1-12200011-2-2003−300−3−3330033−3−30-1-100011000000000000−333−30000
χ5522-2-1222-2-1222211-1-121-2-211-1-12-1-22-1-11122-211-2-2220033−3−3-11-211-1-2-111-1-10011-2-2000-1-12200−330033−3−300−3−333011000-1-1000000000000−333−30000
χ5622-2-1222-2-1222211-1-121-2-211-1-12-1-22-1-11122-211-2-22200−3−333-11-211-1-2-111-1-10011-2-2000-1-122003−300−3−3330033−3−3011000-1-10000000000003−3−330000
χ5722-2-122-22-122-2-2-1-1-1-121-2-211-1-1212-211-1-1-2-22-1-12-22-222-1-1-1-1-11-211-121-1-11100-112-200-2-112-2001122-1-1-1-1-2-211110-11000-110000002-20000-1-1110000
χ5822-2-122-22-122-2-2-1-1-1-121-2-211-1-1212-211-1-1-2-22-1-12-22-2-2-21111-11-211-121-1-11100-112-2002-112-200-1-1-2-2111122-1-1-1-10-11000-11000000-22000011-1-10000
χ5922-2-122-22-122-2-2-1-1-1-121-2-211-1-1212-211-1-1-2-22-1-1-22-2222-1-1-1-1-11-211-121-1-111001-1-2200-21-1-22001122-1-1-1-1-2-2111101-10001-1000000-22000011-1-10000
χ6022-2-122-22-122-2-2-1-1-1-121-2-211-1-1212-211-1-1-2-22-1-1-22-22-2-21111-11-211-121-1-111001-1-220021-1-2200-1-1-2-2111122-1-1-1-101-10001-10000002-20000-1-1110000
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χ624444-2-2444-2-2-2-244-2-214-2-2-2-2-2-214-2-2-2-2-2-211-2-2-200000000001-211111-21111440000-2-200000-2-200000000000000-20011-20011000000000000000000
χ634444-2-2444-2-2-2-244-2-214-2-2-2-2-2-214-2-2-2-2-2-211-2-2-200000000001-211111-21111-4-4000022000002200000000000000200-1-1200-1-1000000000000000000
χ644444-2-2-4-44-2-222-4-4-2-214-2-2-2-2-2-21-4222222-1-122200000000001-21111-12-1-1-1-1000000−2i32i300000−2i32i300000000000000000i3−i3000i3−i3000000000000000000
χ654444-2-2-4-44-2-222-4-4-2-214-2-2-2-2-2-21-4222222-1-122200000000001-21111-12-1-1-1-10000002i3−2i3000002i3−2i300000000000000000−i3i3000−i3i3000000000000000000
χ66444-24-244-2-24-2-2-2-21-2-2-24-2111-2-2-24411-2-2-2-2-211000044-2-2-2-21-2-2111-2-21111000000004000000-2-2-2-21111-2-211110000000000000000000000000000
χ67444-24-244-2-24-2-2-2-21-2-2-24-2111-2-2-24411-2-2-2-2-2110000-4-422221-2-2111-2-2111100000000-40000002222-1-1-1-122-1-1-1-10000000000000000000000000000
χ68444-24-2-4-4-2-2422221-2-2-24-2111-2-22-4-4-1-122222-1-10000002323−23−231-2-211122-1-1-1-100000000000000023−2300−3−33300−3−3330000000000000000000000000000
χ69444-24-2-4-4-2-2422221-2-2-24-2111-2-22-4-4-1-122222-1-1000000−23−2323231-2-211122-1-1-1-1000000000000000−23230033−3−30033−3−30000000000000000000000000000
χ70444-2-2444-24-244-2-2-21-2-2-24-2-2-21-2-2-2-2-2-211-2-24-2-2444400000011-2111-21111100-2-2-2-2000-2-2-2-200000000000000000110001100000000000000000000
χ71444-2-2444-24-244-2-2-21-2-2-24-2-2-21-2-2-2-2-2-211-2-24-2-2-4-4-4-400000011-2111-211111002222000222200000000000000000-1-1000-1-100000000000000000000
χ72444-2-24-4-4-24-2-4-422-21-2-2-24-2-2-21-222222-1-122-4224-4-4400000011-21112-1-1-1-1-100-22-220002-22-2000000000000000001-1000-1100000000000000000000
χ73444-2-24-4-4-24-2-4-422-21-2-2-24-2-2-21-222222-1-122-422-444-400000011-21112-1-1-1-1-1002-22-2000-22-2200000000000000000-110001-100000000000000000000
χ7444-444-24-44-24-2-2-4-4-24-2-4-4222-24-24-44-2-2-4-4-2-22220000000000-2-4222-22422-2-2000000000000000000000000000000000000000000000000000000000
χ7544-44-2-24-44-2-2-2-2-4-4-2-21-42222-2-2142-2-2-22211222000000000012-1-1-11-1-2-1-111000000−2i32i3000002i3−2i300000000000000000i3−i3000−i3i3000000000000000000
χ7644-44-2-24-44-2-2-2-2-4-4-2-21-42222-2-2142-2-2-22211222000000000012-1-1-11-1-2-1-1110000002i3−2i300000−2i32i300000000000000000−i3i3000i3−i3000000000000000000
χ7744-44-2-2-444-2-22244-2-21-42222-2-21-4-2222-2-2-1-1-2-2-2000000000012-1-1-111211-1-14-40000-2-2000002200000000000000-20011200-1-1000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.