Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C5 |
| direct product | C11×C11⋊#64480 |
| unambiguous semidirect product | C11⋊(C11×#64480) |
| Fitting, socle, Hall | C52×C112 ⋊ Dic3 |
| derived | C11×C52⋊C3 ⋊ C4×C11 |
| Hall | C112×C52⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ #64480 |
| Hall | C52⋊C3 ⋊ C11×Dic11 |
| Sylow | C52 ⋊ C11×Dic33 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 702);