Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×#64470 |
| derived, Hall | C52⋊C3 ⋊ C4×C112 |
| Hall | C112×C52⋊C3 ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Sylow | C52 ⋊ C112×Dic3 |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7260 |
3146 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 425);