Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C109 ⋊ C4 |
| Sylow | C109 ⋊ #1436 |
612 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3488 |
Polycyclic presentation:
2^7,109|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^b=h^33,h^g=h^108596 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 19689);