Finite Group Databasebeta

← Group #11774667

Character table — Group #11774667

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order1222444444443366666612121212121212121212121212121212121212122244444466661212121212121212121212124444888824242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111
χ711111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1i−ii−iii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1−ii−ii−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1i−ii−iii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1−ii−ii−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1i−i−iiii−i−i−i−iii-11ii−i−i−i−iii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1−iii−i−i−iiiii−i−i-11−i−iiiii−i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1i−i−iiii−i−i−i−iii-11−i−iiiii−i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1−iii−i−i−iiiii−i−i-11ii−i−i−i−iii
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ192222-2-2-2-222-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2000000000000000000000000-2-222000000000000-2200000000
χ202222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000-2-2220000000000002-200000000
χ2122-2-22i−2i2i−2i0000222-2-22-2-22i−2i2i2i−2i−2i000000002i−2i000000002-22i−2i0000000022-2-22i2i−2i−2i2-22i−2i0000000000000000000000
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χ2422-2-22i−2i2i−2i0000222-2-22-2-22i−2i2i2i−2i−2i000000002i−2i0000-22−2i2i0000-2-222−2i−2i2i2i00000000-22−2i2i0000000000000000000000
χ2522-2-2−2i2i−2i2i0000222-2-22-2-2−2i2i−2i−2i2i2i00000000−2i2i000000002-2−2i2i0000000022-2-2−2i−2i2i2i2-2−2i2i0000000000000000000000
χ2622-2-2−2i2i−2i2i0000222-2-22-2-2−2i2i−2i−2i2i2i00000000−2i2i00000000-222i−2i00000000-2-2222i2i−2i−2i2-2−2i2i0000000000000000000000
χ2722-2-2−2i2i−2i2i0000222-2-22-2-2−2i2i−2i−2i2i2i00000000−2i2i00002-2−2i2i000022-2-2−2i−2i2i2i00000000-222i−2i0000000000000000000000
χ2822-2-2−2i2i−2i2i0000222-2-22-2-2−2i2i−2i−2i2i2i00000000−2i2i0000-222i−2i0000-2-2222i2i−2i−2i00000000-222i−2i0000000000000000000000
χ292-22-22i−2i−2i2i2i−2i2-222-22-2-22-22i−2i2i−2i2i−2i2i2i−2i−2i22-2-2−2i2i2i−2i2-20000000000000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ302-22-22i−2i−2i2i2i−2i2-222-22-2-22-22i−2i2i−2i2i−2i2i2i−2i−2i22-2-2−2i2i2i−2i2-2000000000000000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ312-22-22i−2i−2i2i−2i2i-2222-22-2-22-22i−2i2i−2i2i−2i−2i−2i2i2i-2-222−2i2i−2i2i-220000000000000000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ322-22-22i−2i−2i2i−2i2i-2222-22-2-22-22i−2i2i−2i2i−2i−2i−2i2i2i-2-222−2i2i−2i2i-22000000000000000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ332-22-2−2i2i2i−2i2i−2i-2222-22-2-22-2−2i2i−2i2i−2i2i2i2i−2i−2i-2-2222i−2i2i−2i-220000000000000000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ342-22-2−2i2i2i−2i2i−2i-2222-22-2-22-2−2i2i−2i2i−2i2i2i2i−2i−2i-2-2222i−2i2i−2i-22000000000000000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ352-22-2−2i2i2i−2i−2i2i2-222-22-2-22-2−2i2i−2i2i−2i2i−2i−2i2i2i22-2-22i−2i−2i2i2-20000000000000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ362-22-2−2i2i2i−2i−2i2i2-222-22-2-22-2−2i2i−2i2i−2i2i−2i−2i2i2i22-2-22i−2i−2i2i2-2000000000000000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ374444444444441-2111-2-2-211-2-2-2-2-2-2-2-2-2-2-2-211111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ384444444444441-2111-2-2-211-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-2111111110000000000
χ39444444444444-21-2-2-2111-2-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ40444444444444-21-2-2-2111-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ4144444444-4-4-4-41-2111-2-2-211-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
χ4244444444-4-4-4-41-2111-2-2-211-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2221111-1-1-1-10000000000
χ4344444444-4-4-4-4-21-2-2-2111-2-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ4444444444-4-4-4-4-21-2-2-2111-2-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000000000
χ454444-4-4-4-444-4-41-2111-2-2-2-1-12222-2-2-2-22222-1-111-1-100000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000000000
χ464444-4-4-4-444-4-41-2111-2-2-2-1-12222-2-2-2-22222-1-111-1-10000000000000000000000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ474444-4-4-4-444-4-4-21-2-2-211122-1-1-1-11111-1-1-1-122-2-22222-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000000000
χ484444-4-4-4-444-4-4-21-2-2-211122-1-1-1-11111-1-1-1-122-2-222-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000000000
χ494444-4-4-4-4-4-4441-2111-2-2-2-1-122222222-2-2-2-2-1-1-1-11100000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000000000
χ504444-4-4-4-4-4-4441-2111-2-2-2-1-122222222-2-2-2-2-1-1-1-1110000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000000000
χ514444-4-4-4-4-4-444-21-2-2-211122-1-1-1-1-1-1-1-111112222-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ524444-4-4-4-4-4-444-21-2-2-211122-1-1-1-1-1-1-1-111112222-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
χ5344-4-44i−4i4i−4i0000-21-2221-1-1−2i2iii−i−i3-33-33i−3i3i−3i−2i2i00002-22i−2i2-22i−2i-1-111−i−iii-1-111−i−iii00000000000000000000000000
χ5444-4-44i−4i4i−4i0000-21-2221-1-1−2i2iii−i−i3-33-33i−3i3i−3i−2i2i0000-22−2i2i-22−2i2i11-1-1ii−i−i11-1-1ii−i−i00000000000000000000000000
χ5544-4-44i−4i4i−4i0000-21-2221-1-1−2i2iii−i−i-33-33−3i3i−3i3i−2i2i00002-22i−2i-22−2i2i-1-111−i−iii11-1-1ii−i−i00000000000000000000000000
χ5644-4-44i−4i4i−4i0000-21-2221-1-1−2i2iii−i−i-33-33−3i3i−3i3i−2i2i0000-22−2i2i2-22i−2i11-1-1ii−i−i-1-111−i−iii00000000000000000000000000
χ5744-4-4−4i4i−4i4i0000-21-2221-1-12i−2i−i−iii3-33-3−3i3i−3i3i2i−2i00002-2−2i2i2-2−2i2i-1-111ii−i−i-1-111ii−i−i00000000000000000000000000
χ5844-4-4−4i4i−4i4i0000-21-2221-1-12i−2i−i−iii3-33-3−3i3i−3i3i2i−2i0000-222i−2i-222i−2i11-1-1−i−iii11-1-1−i−iii00000000000000000000000000
χ5944-4-4−4i4i−4i4i0000-21-2221-1-12i−2i−i−iii-33-333i−3i3i−3i2i−2i00002-2−2i2i-222i−2i-1-111ii−i−i11-1-1−i−iii00000000000000000000000000
χ6044-4-4−4i4i−4i4i0000-21-2221-1-12i−2i−i−iii-33-333i−3i3i−3i2i−2i0000-222i−2i2-2−2i2i11-1-1−i−iii-1-111ii−i−i00000000000000000000000000
χ614-44-44i−4i−4i4i4i−4i4-41-2-11-12-22i−i−2i2i−2i2i−2i−2i2i2i-2-222−iii−i1-100000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ624-44-44i−4i−4i4i4i−4i4-41-2-11-12-22i−i−2i2i−2i2i−2i−2i2i2i-2-222−iii−i1-100000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ634-44-44i−4i−4i4i4i−4i4-4-212-22-11-1−2i2ii−ii−iii−i−i11-1-12i−2i−2i2i-2200000000−i3i3−i3i33−33−33−33−3−i3i3−i3i300000000000000000000000000
χ644-44-44i−4i−4i4i4i−4i4-4-212-22-11-1−2i2ii−ii−iii−i−i11-1-12i−2i−2i2i-2200000000i3−i3i3−i3−33−33−33−33i3−i3i3−i300000000000000000000000000
χ654-44-44i−4i−4i4i−4i4i-441-2-11-12-22i−i−2i2i−2i2i2i2i−2i−2i22-2-2−ii−ii-1100000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ664-44-44i−4i−4i4i−4i4i-441-2-11-12-22i−i−2i2i−2i2i2i2i−2i−2i22-2-2−ii−ii-1100000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ674-44-44i−4i−4i4i−4i4i-44-212-22-11-1−2i2ii−ii−i−i−iii-1-1112i−2i2i−2i2-200000000−i3i3−i3i33−33−3−33−33i3−i3i3−i300000000000000000000000000
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χ694-44-4−4i4i4i−4i4i−4i-441-2-11-12-22−ii2i−2i2i−2i−2i−2i2i2i22-2-2i−ii−i-1100000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ704-44-4−4i4i4i−4i4i−4i-441-2-11-12-22−ii2i−2i2i−2i−2i−2i2i2i22-2-2i−ii−i-1100000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ714-44-4−4i4i4i−4i4i−4i-44-212-22-11-12i−2i−ii−iiii−i−i-1-111−2i2i−2i2i2-200000000−i3i3−i3i3−33−333−33−3i3−i3i3−i300000000000000000000000000
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χ734-44-4−4i4i4i−4i−4i4i4-41-2-11-12-22−ii2i−2i2i−2i2i2i−2i−2i-2-222i−i−ii1-100000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ744-44-4−4i4i4i−4i−4i4i4-41-2-11-12-22−ii2i−2i2i−2i2i2i−2i−2i-2-222i−i−ii1-100000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
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χ774-4-4444-4-4000044-4-44-4-44444-4-4400000000-4-4000000000000000000000000000000000000000000000000000000
χ784-4-4444-4-40000-2122-2-1-11-2-21-1-113i−3i−3i3i−3i3i3i−3i22000000000000−i3i3i3−i3−i3i3i3−i33−3−33−333−300000000000000000000000000
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χ804-4-4444-4-40000-2122-2-1-11-2-21-1-11−3i3i3i−3i3i−3i−3i3i22000000000000−i3i3i3−i3−i3i3i3−i3−333−33−3−3300000000000000000000000000
χ814-4-4444-4-40000-2122-2-1-11-2-21-1-11−3i3i3i−3i3i−3i−3i3i22000000000000i3−i3−i3i3i3−i3−i3i33−3−33−333−300000000000000000000000000
χ824-4-44-4-444000044-4-44-4-44-4-4-444-40000000044000000000000000000000000000000000000000000000000000000
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χ844-4-44-4-4440000-2122-2-1-1122-111-13i−3i−3i3i3i−3i−3i3i-2-2000000000000i3−i3−i3i3−i3i3i3−i3−333−3−333−300000000000000000000000000
χ854-4-44-4-4440000-2122-2-1-1122-111-1−3i3i3i−3i−3i3i3i−3i-2-2000000000000−i3i3i3−i3i3−i3−i3i3−333−3−333−300000000000000000000000000
χ864-4-44-4-4440000-2122-2-1-1122-111-1−3i3i3i−3i−3i3i3i−3i-2-2000000000000i3−i3−i3i3−i3i3i3−i33−3−333−3−3300000000000000000000000000
χ8788-8-88i−8i8i−8i00002-42-2-2-4442i−2i−4i−4i4i4i000000002i−2i000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i8i−8i8i00002-42-2-2-444−2i2i4i4i−4i−4i00000000−2i2i000000000000000000000000000000000000000000000000000000
χ898-8-8888-8-800002-4-2-2244-422-444-400000000-2-2000000000000000000000000000000000000000000000000000000
χ908-8-88-8-88800002-4-2-2244-4-2-24-4-440000000022000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.