Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C3×#17987504 |
| Fitting | C32×C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ C3×#6909 |
1196 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1539 |
699 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 3922);