Finite Group DatabasebetaFinite Group Databasebeta| order | 13696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C107 ⋊ C2 |
| Sylow | C107 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1712 |
Polycyclic presentation:
2^7,107|b^a=bd,c^a=ce,f^a=fg,h^a=h^106,c^b=cg,e^b=efg,d^c=df,e^d=eg1024 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 6511);