Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C3⋊#14559051 |
| unambiguous semidirect product | C3⋊(C5×#14559051) |
| derived, Hall | C3×C112 ⋊ C4×C52 |
| Hall | C3×C5×#10597243 ⋊ C4 |
| Hall | C5×#10597243 ⋊ Dic3 |
| Hall | C3⋊(C11⋊Dic11) ⋊ C52 |
| Sylow | C112 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C5×#14559051 |
672 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7260 |
510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 389);