Finite Group DatabasebetaFinite Group Databasebeta| order | 13696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #346×C107 ⋊ C2 |
| Sylow | C107 ⋊ #2164 |
138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6848 |
Polycyclic presentation:
2^7,107|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^106,c^b=cg,h^b=h^1062176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 6318);