Finite Group Databasebeta

← Group #13170556

Character table — Group #13170556

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11222222222222244444444444444444444444666666666688888888888812121212121212121212121212121212121212121212121212121212122424242424242424242436363636363636363636363636367272108108
order1223334466666121233366666666612121212121212121212122244882424242436666121212121212122266666666812121212242424242424242424242424242466666666121224446688121224242424121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-111111-1-1-1-11111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111
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
χ911-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-1111111-11-11111111-1-1-111-1-111-1-11-11-11-111-1-1-11-11-1-1-1111111-1-1-1-1-1-11-11-111-1-11-11-11-1111-1-1-111-1-11-1-11
χ1011-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-1111111-11-11111111-1-1-111-1-111-1-1-111-11-1-1-111-11-11-1-1-1111111-1-1-1-1-1-1-111-1-1-1111-1-11-11-1-11-11111-1-1-111-1
χ1111-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-1111111-11-1-1-1-1-1-1-11-1-1-111-1-111-1-11-11-11-111-1-111-11-111-1-1-1-1-1-11111111-11-111-1-11-11-1-1111-11-1-1-1-111-111-1
χ1211-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-1111111-11-1-1-1-1-1-1-11-1-1-111-1-111-1-1-111-11-1-1-11111-11-111-1-1-1-1-1-1111111-111-1-1-1111-1-111-1-1-1-1111-1-1111-1-11
χ1311-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-111111-11-111111111-1-1-111-1-111-1-11-1-11-1111-1-1-1-11-11-1-1111111-1-1-1-1-1-11-1-1111-1-1-11-111-1-1-1-1111-1-1111-11-1
χ1411-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-111111-11-111111111-1-1-111-1-111-1-1-11-11-11-1-111-1-11-11-1-1111111-1-1-1-1-1-1-11-11-1-111-111-1-1111-11-1-1-1-111-11-11
χ1511-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-111111-11-11-1-1-1-1-1-11-1-1-111-1-111-1-11-1-11-1111-1-11-11-1111-1-1-1-1-1-11111111-1-1111-1-1-11-11-11-1-11-11111-1-1-11-11
χ1611-1111-11-1-111111111-1-1-1-1-1-1111-11-1-1-1-111111-11-11-1-1-1-1-1-11-1-1-111-1-111-1-1-11-11-11-1-1111-11-1111-1-1-1-1-1-1111111-11-11-1-111-111-11-1111-1-1-111-1-11-11-1
χ17222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-22-2-2200000022222-2-2-2-2-2-2-2002-22-200000-22-2200000000000000002-20000-22000000000000000000
χ18222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-200000022222-2-2-2-2-2-2-200-22-22000002-22-20000000000000000-2200002-2000000000000000000
χ1922222-122222-12222-1-12-122-1-12-1-12-1-1222-1-12222222000000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1022-1-10000000000000022-1-1-1-1-1-1-1-12200-1-100-1-100000000
χ2022222-122222-12222-1-12-122-1-12-1-12-1-1222-1-12222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-222-1-11111022-1-100000000000000-2-2-1-11111-1-1-2-20011001100000000
χ2122222-122222-12222-1-12-122-1-12-1-12-1-1222-1-1222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-122-2-211-1-1-1-10-2-211000000000000002211-1-1-1-111-2-20011001100000000
χ2222222-122222-12222-1-12-122-1-12-1-12-1-1222-1-1222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111110-2-21100000000000000-2-2111111112200-1-100-1-100000000
χ2322222-1-2-2222-12-2-22-1-12-122-1-12-1-1-211-2-2-211-2-2-22-2-22000000-1-1-1-1-11111111002-2-11−i3i3−i3i30-221-10000000000000000-11−i3i3−i3i31-10000−i3i300−i3i300000000
χ2422222-1-2-2222-12-2-22-1-12-122-1-12-1-1-211-2-2-211-2-2-22-2-22000000-1-1-1-1-11111111002-2-11i3−i3i3−i30-221-10000000000000000-11i3−i3i3−i31-10000i3−i300i3−i300000000
χ2522222-1-2-2222-12-2-22-1-12-122-1-12-1-1-211-2-2-211-2-2-2-222-2000000-1-1-1-1-1111111100-221-1−i3i3−i3i302-2-1100000000000000001-1−i3i3−i3i3-110000i3−i300i3−i300000000
χ2622222-1-2-2222-12-2-22-1-12-122-1-12-1-1-211-2-2-211-2-2-2-222-2000000-1-1-1-1-1111111100-221-1i3−i3i3−i302-2-1100000000000000001-1i3−i3i3−i3-110000−i3i300−i3i300000000
χ272222-1222-1-122-122-12-122-1-1-1-1-1-12222-1-1-122-1-1-10000222222-12-1-1-1-1-12-1-1-1-122000022222000022-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1-10000220000000000-1-100
χ282222-1222-1-122-122-12-122-1-1-1-1-1-12222-1-1-122-1-1-10000222222-12-1-1-1-1-12-1-1-1-1-2-20000-2-2-2-22000022-1-1-1-1-1-1-1-1-1-1-1-1110011110000-2-200000000001100
χ292222-1222-1-122-122-12-122-1-1-1-1-1-12222-1-1-122-1-1-10000-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-12200002222-20000-2-2111111111111-1-100-1-1-1-10000-2-200000000001100
χ302222-1222-1-122-122-12-122-1-1-1-1-1-12222-1-1-122-1-1-10000-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-1-2-20000-2-2-2-2-20000-2-2111111111111110011110000220000000000-1-100
χ31222-1222222-122-1-1-1-12-12-1-122-12-1-1222-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-122-1-1-1-1-100-1-12200002-1-122-1-122-1-1-1-122-1-1-1-100-1-10000-1-10000002200-1-1-1-10000
χ32222-1222222-122-1-1-1-12-12-1-122-12-1-1222-1-1-1-12-1-12222-2-21111-1-1-1-1-122-1-1-1-1-100-1-1220000-2-1-12211-2-21111-2-2111100-1-10000-1-1000000-2-20011110000
χ33222-1222222-122-1-1-1-12-12-1-122-12-1-1222-1-1-1-12-1-1-2-2-2-222-1-1-1-1-1-1-1-1-122-1-1-1-1-10011-2-20000211-2-2-1-122-1-1-1-122-1-1-1-10011000011000000-2-20011110000
χ34222-1222222-122-1-1-1-12-12-1-122-12-1-1222-1-1-1-12-1-1-2-2-2-2-2-21111-1-1-1-1-122-1-1-1-1-10011-2-20000-211-2-211-2-21111-2-2111100110000110000002200-1-1-1-10000
χ35222-122-2-222-12211-1-12-12-1-122-12-11-2-2-21111-2112-2-220033−3−3-1-1-1-1-1-2-21111100-112-2000001-1-223−30033−3−30033−3−300-1100001-100000000003−33−30000
χ36222-122-2-222-12211-1-12-12-1-122-12-11-2-2-21111-2112-2-2200−3−333-1-1-1-1-1-2-21111100-112-2000001-1-22−3300−3−33300−3−33300-1100001-10000000000−33−330000
χ37222-122-2-222-12211-1-12-12-1-122-12-11-2-2-21111-211-222-20033−3−3-1-1-1-1-1-2-211111001-1-2200000-112-23−30033−3−30033−3−3001-10000-110000000000−33−330000
χ38222-122-2-222-12211-1-12-12-1-122-12-11-2-2-21111-211-222-200−3−333-1-1-1-1-1-2-211111001-1-2200000-112-2−3300−3−33300−3−333001-10000-1100000000003−33−30000
χ3922-22222-2-2-2222-2-2222-2-2-2-2-2-22222-22222-2-2-2-2-222-2-20000002-2-2-22-222-2-22200222200000-2-2-2-20000000000000000220000-2-2000000000000000000
χ4022-22222-2-2-2222-2-2222-2-2-2-2-2-22222-22222-2-2-2-2-2-2-2220000002-2-2-22-222-2-22200-2-2-2-20000022220000000000000000-2-2000022000000000000000000
χ4122-222-12-2-2-22-12-2-22-1-1-21-2-2112-1-121-122211-2-2-222-2-2000000-1111-11-1-111-1-10022-1-1−i3i3i3−i30-2-2110000000000000000-1-1−i3i3i3−i3110000−i3i300i3−i300000000
χ4222-222-12-2-2-22-12-2-22-1-1-21-2-2112-1-121-122211-2-2-222-2-2000000-1111-11-1-111-1-10022-1-1i3−i3−i3i30-2-2110000000000000000-1-1i3−i3−i3i3110000i3−i300−i3i300000000
χ4322-222-12-2-2-22-12-2-22-1-1-21-2-2112-1-121-122211-2-2-2-2-222000000-1111-11-1-111-1-100-2-211−i3i3i3−i3022-1-1000000000000000011−i3i3i3−i3-1-10000i3−i300−i3i300000000
χ4422-222-12-2-2-22-12-2-22-1-1-21-2-2112-1-121-122211-2-2-2-2-222000000-1111-11-1-111-1-100-2-211i3−i3−i3i3022-1-1000000000000000011i3−i3−i3i3-1-10000−i3i300i3−i300000000
χ4522-222-1-22-2-22-12222-1-1-21-2-2112-1-1-2-11-2-2-2-1-12222-22-2000000-1111-1-111-1-1112-22-2-11-1-11102-2-11000000000000002-2-11-1-111-112-200-1-1001100000000
χ4622-222-1-22-2-22-12222-1-1-21-2-2112-1-1-2-11-2-2-2-1-12222-22-2000000-1111-1-111-1-111-222-2-1111-1-102-2-1100000000000000-22-1111-1-1-11-22001100-1-100000000
χ4722-222-1-22-2-22-12222-1-1-21-2-2112-1-1-2-11-2-2-2-1-1222-22-22000000-1111-1-111-1-1112-2-221-1-1-1110-221-1000000000000002-21-1-1-1111-1-22001100-1-100000000
χ4822-222-1-22-2-22-12222-1-1-21-2-2112-1-1-2-11-2-2-2-1-1222-22-22000000-1111-1-111-1-111-22-221-111-1-10-221-100000000000000-221-111-1-11-12-200-1-1001100000000
χ4922-22-12-221122-122-12-1-2-21111-1-12-22-211122-1-1-10000222222-1-211-1-11-2-1-1112-2000022-2-2-20000-2-2-1-1-1-1-1-1111111-1100-1-11100002-20000000000-1100
χ5022-22-12-221122-122-12-1-2-21111-1-12-22-211122-1-1-10000222222-1-211-1-11-2-1-111-220000-2-222-20000-2-2-1-1-1-1-1-11111111-10011-1-10000-2200000000001-100
χ5122-22-12-221122-122-12-1-2-21111-1-12-22-211122-1-1-10000-2-2-2-2-2-2-1-211-1-11-2-1-1112-2000022-2-22000022111111-1-1-1-1-1-1-1100-1-1110000-2200000000001-100
χ5222-22-12-221122-122-12-1-2-21111-1-12-22-211122-1-1-10000-2-2-2-2-2-2-1-211-1-11-2-1-111-220000-2-2222000022111111-1-1-1-1-1-11-10011-1-100002-20000000000-1100
χ5322-2-1222-2-2-2-12211-1-121-211-2-2-12-1-1-222-1-111-21122-2-20033−3−3-1111-1-22-111-1-100-1-1220000011-2-2−330033−3−300−3−33300-1-100001100000000003−3−330000
χ5422-2-1222-2-2-2-12211-1-121-211-2-2-12-1-1-222-1-111-21122-2-200−3−333-1111-1-22-111-1-100-1-1220000011-2-23−300−3−3330033−3−300-1-10000110000000000−333−30000
χ5522-2-1222-2-2-2-12211-1-121-211-2-2-12-1-1-222-1-111-211-2-2220033−3−3-1111-1-22-111-1-10011-2-200000-1-122−330033−3−300−3−33300110000-1-10000000000−333−30000
χ5622-2-1222-2-2-2-12211-1-121-211-2-2-12-1-1-222-1-111-211-2-22200−3−333-1111-1-22-111-1-10011-2-200000-1-1223−300−3−3330033−3−300110000-1-100000000003−3−330000
χ5722-2-122-22-2-2-122-1-1-1-121-211-2-2-12-112-2-211-1-12-1-12-22-222-1-1-1-1-1111-12-21-1-11100-112-20000-2-112-21122-1-1-1-1-2-2111100-110000-110000002-200-1-1110000
χ5822-2-122-22-2-2-122-1-1-1-121-211-2-2-12-112-2-211-1-12-1-12-22-2-2-21111-1111-12-21-1-11100-112-200002-112-2-1-1-2-2111122-1-1-1-100-110000-11000000-220011-1-10000
χ5922-2-122-22-2-2-122-1-1-1-121-211-2-2-12-112-2-211-1-12-1-1-22-2222-1-1-1-1-1111-12-21-1-111001-1-220000-21-1-221122-1-1-1-1-2-21111001-100001-1000000-220011-1-10000
χ6022-2-122-22-2-2-122-1-1-1-121-211-2-2-12-112-2-211-1-12-1-1-22-22-2-21111-1111-12-21-1-111001-1-22000021-1-22-1-1-2-2111122-1-1-1-1001-100001-10000002-200-1-1110000
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χ624444-2-244-2-24-2-244-2-214-2-2-211-21-24-2-2-2-2-2-2-2-2-2-200000000001-211111-21111440000-2-2-2-20000000000000000000-2-200111100000000000000000000
χ634444-2-244-2-24-2-244-2-214-2-2-211-21-24-2-2-2-2-2-2-2-2-2-200000000001-211111-21111-4-40000222200000000000000000002200-1-1-1-100000000000000000000
χ644444-2-2-4-4-2-24-2-2-4-4-2-214-2-2-211-21-2-4222222222200000000001-2111-1-12-1-1-1-1000000−2i32i3−2i32i300000000000000000000000i3−i3i3−i300000000000000000000
χ654444-2-2-4-4-2-24-2-2-4-4-2-214-2-2-211-21-2-4222222222200000000001-2111-1-12-1-1-1-10000002i3−2i32i3−2i300000000000000000000000−i3i3−i3i300000000000000000000
χ66444-24-24444-2-24-2-2-21-2-2-2-2-2-2-2-2-21-2-2-24-2-2114-2-2444400000011111-2-21111100-2-2-2-200000-2-2-2-2000000000000000011000011000000000000000000
χ67444-24-24444-2-24-2-2-21-2-2-2-2-2-2-2-2-21-2-2-24-2-2114-2-2-4-4-4-400000011111-2-2111110022220000022220000000000000000-1-10000-1-1000000000000000000
χ68444-24-2-4-444-2-2422-21-2-2-2-2-2-2-2-2-21222-422-1-1-4224-4-440000001111122-1-1-1-1-100-22-22000002-22-200000000000000001-10000-11000000000000000000
χ69444-24-2-4-444-2-2422-21-2-2-2-2-2-2-2-2-21222-422-1-1-422-444-40000001111122-1-1-1-1-1002-22-200000-22-220000000000000000-1100001-1000000000000000000
χ70444-2-2444-2-2-24-2-2-21-2-2-2411-2-21-2-2-244-211-2-2-211000044-2-2-2-21-2111-2-2-21111000000000040000-2-2-2-21111-2-211110000000000000000000000000000
χ71444-2-2444-2-2-24-2-2-21-2-2-2411-2-21-2-2-244-211-2-2-2110000-4-422221-2111-2-2-211110000000000-400002222-1-1-1-122-1-1-1-10000000000000000000000000000
χ72444-2-24-4-4-2-2-24-2221-2-2-2411-2-21-2-22-4-42-1-1222-1-10000002323−23−231-2111222-1-1-1-100000000000000023−2300−3−33300−3−3330000000000000000000000000000
χ73444-2-24-4-4-2-2-24-2221-2-2-2411-2-21-2-22-4-42-1-1222-1-1000000−23−2323231-2111222-1-1-1-1000000000000000−23230033−3−30033−3−30000000000000000000000000000
χ7444-44-244-42244-2-4-4-24-2-4-42222-2-244-44-2-2-2-4-42220000000000-2-422-22-2422-2-2000000000000000000000000000000000000000000000000000000000
χ7544-44-2-24-4224-2-2-4-4-2-21-4222-1-1-21-242-2-2-2-222222000000000012-1-11-11-2-1-111000000−2i32i32i3−2i300000000000000000000000i3−i3−i3i300000000000000000000
χ7644-44-2-24-4224-2-2-4-4-2-21-4222-1-1-21-242-2-2-2-222222000000000012-1-11-11-2-1-1110000002i3−2i3−2i32i300000000000000000000000−i3i3i3−i300000000000000000000
χ7744-44-2-2-44224-2-244-2-21-4222-1-1-21-2-4-22222-2-2-2-2-2000000000012-1-111-1211-1-14-40000-2-2220000000000000000000-220011-1-100000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.