Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C5 |
| direct product | C11×C3⋊(C11⋊#1044) |
| unambiguous semidirect product | C3⋊(C11×C11⋊#1044) |
| unambiguous semidirect product | C11⋊(C11×C3⋊#1044) |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C4 |
| derived | C3×C52×C11 ⋊ C4×C11 |
| Hall | C52×C112 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #1044 |
| Sylow | C112 ⋊ C3⋊#1044 |
| Hall | C3×C52 ⋊ C11×Dic11 |
| Sylow | C52 ⋊ C11×Dic33 |
| Sylow | C3 ⋊ C11×C11⋊#1044 |
288 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
2574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 943);