Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C101 ⋊ C4 |
| Sylow | C101 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 1616 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2,8,4)(3,6,18,14)(5,7,16,10)(9,12,32,24)(11,17,28,20)(13,15,30,26)(19,22,50,38)(21,31,42,34)(23,25,48,44)(27,29,46,40)(33,36,69,56)(35,49,53,52)(37,39,68,60)(41,47,64,58)(43,45,66,62)(51,54,67,71)(55,57,83,74)(59,61,82,78)(63,65,80,76)(70,72,81,85)(73,75,93,88)(77,79,92,90)(84,86,91,95)(87,89,99,97)(94,96,98,101)(102,104,112,115,106,113,105,111)(103,108,110,107,109,117,114,116);(102,103)(104,108)(105,114)(106,109)(107,115)(110,112)(111,116)(113,117);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,54,58)(45,59,60,48)(46,47,63,62)(57,70,71,69)(61,73,74,68)(64,67,72,76)(65,77,78,66)(75,84,85,83)(79,87,88,82)(80,81,86,90)(89,94,95,93)(91,96,97,92)(98,100,101,99)(103,107,109,116)(104,111)(105,112)(108,114,117,110)(113,115)Polycyclic presentation:
2^7,101|a^2=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^10,d^b=dfg,e^b=eg,f^b=fg,d^c=dg,h^c=h^91,h^e=h^100298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20920);