Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C41×ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C3×C5×AGL(1,𝔽5)×C41) |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C4 |
| derived | C3×C5 ⋊ C3×C4×C5×C41 |
| Hall | C52×C41 ⋊ C3×Dic3 |
| Hall | C32×C41 ⋊ C5×AGL(1,𝔽5) |
| Hall | C32×C52 ⋊ C4×C41 |
| Sylow | C52 ⋊ C3×Dic3×C41 |
| Sylow | C32 ⋊ C5×AGL(1,𝔽5)×C41 |
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2460 |
5535 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 514);