Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C101 ⋊ C4 |
| Sylow | C101 ⋊ #1402 |
122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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 — 2 generators on 117 points:
(1,3)(2,6)(4,13)(5,12)(7,10)(8,16)(9,15)(11,14)(17,18,21,26,35,48,65,58,41,28,19,23,30,39,52,69,84,75,54,37,24,32,43,56,73,88,99,90,71,50,33,45,60,77,92,103,110,101,86,67,46,62,80,95,106,113,115,108,97,82,63,81,96,107,114,117,116,112,105,94,79,61,78,93,104,111,109,102,91,76,59,44,57,74,89,100,98,87,72,55,42,31,40,53,70,85,83,68,51,38,29,22,27,36,49,66,64,47,34,25,20);(1,2)(3,10,11,6)(4,8,14,7)(5,9)(12,16,13,15)(18,19,20,22)(21,24,25,31)(23,28,29,27)(26,33,34,44)(30,37,38,40)(32,41,42,36)(35,46,47,61)(39,50,51,57)(43,54,55,53)(45,58,59,49)(48,63,64,81)(52,67,68,78)(56,71,72,74)(60,75,76,70)(62,65,79,66)(69,82,83,96)(73,86,87,93)(77,90,91,89)(80,84,94,85)(88,97,98,107)(92,101,102,104)(95,99,105,100)(103,108,109,114)(106,110,112,111)(113,115,116,117)Polycyclic presentation:
2^7,101|a^2=d,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^10,d^b=deg,e^b=eg,f^b=fg,d^c=dfg,e^c=eg,e^d=eg,h^d=h^100442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19629);