Finite Group Databasebeta

← Group #13155700

Character table — Group #13155700

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order1222333446666666661212121233366666666612121212121212121212121236661212121212124488882424242424242424242424242424242424242424242424242424242424242424444412121212121212124444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-11-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−i1-11-111-1-11-1i−iii−i−ii−i1-1i−i
χ1011-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-11-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−ii1-11-111-1-11-1−ii−i−iii−ii1-1−ii
χ1111-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-1-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−ii1-11-111-1-1-11i−i−i−iiii−i-11−ii
χ1211-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-1-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−i1-11-111-1-1-11−iiii−i−i−ii-11i−i
χ1311-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-111-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−i-11-11-1-111-11−iiii−i−i−ii-11−ii
χ1411-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-111-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−ii-11-11-1-111-11i−i−i−iiii−i-11i−i
χ1511-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-11-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−ii-11-11-1-1111-1−ii−i−iii−ii1-1i−i
χ1611-1-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-11-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−i-11-11-1-1111-1i−iii−i−ii−i1-1−ii
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-20000000000002-22-2000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-222000000000000-22-22000000
χ19222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ20222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ21222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ22222222-122222-12-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ23222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−33−33−30033−3−30033−3−30033−3−30033−3−322-2-2000000000000-11-11000000
χ24222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-2220000000000001-11-1000000
χ25222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-2-2220000000000001-11-1000000
χ26222222-1-2-2222-12-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−33−33−3300−3−33300−3−33300−3−33300−3−33322-2-2000000000000-11-11000000
χ2722222-122222-12-122-122222-12-1-1-122-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-100220000-1-10000
χ2822222-122222-12-122-122222-12-1-1-122-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-20000000000001111111111110000-1-122-1-1-1-100-2-20000110000
χ2922222-122222-12-122-122222-12-1-1-122-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000011-2-2111100-2-20000110000
χ3022222-122222-12-122-122222-12-1-1-122-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-2000000000000111111111111000011-2-2111100220000-1-10000
χ312222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1-1-12200000000-1-100
χ322222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-20000111111111111000000000000000022-1-1-1-1-1-1-2-2000000001100
χ332222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2111111-2-2000000001100
χ342222-12222-1-1222222-12222-1-12-1-1-1-122-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200001111111111110000000000000000-2-21111112200000000-1-100
χ3522-2-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-22-2-2222-2-2-2222-2-22-22-2-222000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ3622-2-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-22-2-2222-2-2-2222-2-22-22-2-22200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ3722-2-222-12-2-2-2-2-1211-22-1-1112-1-1-2-21111-1-122-2-1-111-22-1-111-111-12-2-1-111002-22i−2i-1-111−i−iii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i−2i2i−2i000000000000−i−iii000000
χ3822-2-222-12-2-2-2-2-1211-22-1-1112-1-1-2-21111-1-122-2-1-111-22-1-111-111-12-2-1-111002-2−2i2i-1-111ii−i−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i2i−2i2i000000000000ii−i−i000000
χ3922-2-222-12-2-2-2-2-1211-22-1-1112-1-1-2-21111-1-122-2-1-111-22-1-111-111-12-2-1-11100-222i−2i11-1-1−i−iii-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i2i−2i2i000000000000ii−i−i000000
χ4022-2-222-12-2-2-2-2-1211-22-1-1112-1-1-2-21111-1-122-2-1-111-22-1-111-111-12-2-1-11100-22−2i2i11-1-1ii−i−i-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i−2i2i−2i000000000000−i−iii000000
χ4122-2-222-1-22-2-2-2-1211-2211-1-12-1-1-2-21111-1-12-2211-1-12-211-1-1-111-1-2211-1-10000003−3−33−i3i3i3−i30033−3−300−3−33300−i3−i3i3i300i3i3−i3−i3−2i2i2i−2i000000000000i−i−ii000000
χ4222-2-222-1-22-2-2-2-1211-2211-1-12-1-1-2-21111-1-12-2211-1-12-211-1-1-111-1-2211-1-10000003−3−33i3−i3−i3i30033−3−300−3−33300i3i3−i3−i300−i3−i3i3i32i−2i−2i2i000000000000−iii−i000000
χ4322-2-222-1-22-2-2-2-1211-2211-1-12-1-1-2-21111-1-12-2211-1-12-211-1-1-111-1-2211-1-1000000−333−3−i3i3i3−i300−3−3330033−3−300−i3−i3i3i300i3i3−i3−i32i−2i−2i2i000000000000−iii−i000000
χ4422-2-222-1-22-2-2-2-1211-2211-1-12-1-1-2-21111-1-12-2211-1-12-211-1-1-111-1-2211-1-1000000−333−3i3−i3−i3i300−3−3330033−3−300i3i3−i3−i300−i3−i3i3i3−2i2i2i−2i000000000000i−i−ii000000
χ4522-2-22-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1-2-1-1-2-2122211-111-1-11-1-1112-2002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000-112-2-1-111002i−2i0000−ii0000
χ4622-2-22-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1-2-1-1-2-2122211-111-1-11-1-1112-200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000-112-2-1-11100−2i2i0000i−i0000
χ4722-2-22-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1-2-1-1-2-2122211-111-1-11-1-111-22002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii00001-1-2211-1-100−2i2i0000i−i0000
χ4822-2-22-122-2-2-212-1-2-21222-2-2-12-111-2-2112-1-1-1-2-1-1-2-2122211-111-1-11-1-111-2200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i00001-1-2211-1-1002i−2i0000−ii0000
χ4922-2-2-1222-211-222-2-2-2-122-2-2-1-121111-2-2-12-1212211-2-1-1-1-2-2-111-1-11-1-1112-22-20022-2-20000-1-1-1-1-1-111111100000000000000002-2-11-1-1112-200000000-1100
χ5022-2-2-1222-211-222-2-2-2-122-2-2-1-121111-2-2-12-1212211-2-1-1-1-2-2-111-1-11-1-1112-2-2200-2-2220000111111-1-1-1-1-1-100000000000000002-2-11-1-111-22000000001-100
χ5122-2-2-1222-211-222-2-2-2-122-2-2-1-121111-2-2-12-1212211-2-1-1-1-2-2-111-1-11-1-111-222-20022-2-20000-1-1-1-1-1-11111110000000000000000-221-111-1-1-22000000001-100
χ5222-2-2-1222-211-222-2-2-2-122-2-2-1-121111-2-2-12-1212211-2-1-1-1-2-2-111-1-11-1-111-22-2200-2-2220000111111-1-1-1-1-1-10000000000000000-221-111-1-12-200000000-1100
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χ634444-2-2444-2-2-24-244-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111440000000000000000000000000000000000000000-2-2-2-2111100000000000000
χ644444-2-2444-2-2-24-244-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-400000000000000000000000000000000000000002222-1-1-1-100000000000000
χ654444-2-24-4-4-2-2-24-244-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000003-33-300000000000000
χ664444-2-24-4-4-2-2-24-244-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000000-33-3300000000000000
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χ6844-4-44-2-24-4-4-42-2-22224-2-222-2-212222-1-1-21-2-2-4112224-2-2-1-11-1-11-2211-1-100004i−4i0000−2i−2i2i2i000000000000−2i−2iiiii2i2i−i−i−i−i00000000000000000000000000
χ6944-4-44-2-24-4-4-42-2-22224-2-222-2-212222-1-1-21-2-2-4112224-2-2-1-11-1-11-2211-1-10000−4i4i00002i2i−2i−2i0000000000002i2i−i−i−i−i−2i−2iiiii00000000000000000000000000
χ7044-4-44-2-2-44-4-42-2-2222422-2-2-2-212222-1-1-21-224-1-1-2-2-2-422111-1-112-2-1-1110000000000−2i32i32i3−2i300000000000000i3i3−i3−i300−i3−i3i3i300000000000000000000000000
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χ7344-4-4-24-24-422-4-2422-4-2-2-222-21-222-1-1221-2-242-2-2-1-1-4-211221-1-11-2211-1-1004-400-2-2220000-2-2111122-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.