Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C5×(C11⋊C5)⋊Dic11 |
| unambiguous semidirect product | (C11⋊C5)⋊(C3×C5×Dic11) |
| derived, Sylow | C112 ⋊ C3×C4×C52 |
| Hall | C3×C5×C11×C11⋊C5 ⋊ C4 |
| Hall | C5×C11×C11⋊C5 ⋊ C3×C4 |
| Hall | C3×C11⋊Dic11 ⋊ C52 |
| Hall | C11⋊Dic11 ⋊ C3×C52 |
| Hall | C3×C112 ⋊ C4×C52 |
216 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3300 |
1380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 369);