Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×Dic3×#10597243 |
| unambiguous semidirect product | C3⋊(C4×C5×#10597243) |
| derived, Hall | C3×C112 ⋊ C4×C52 |
| Hall | C3×C5×#10597243 ⋊ C4 |
| Hall | C112×Dic3 ⋊ C52 |
| Sylow | C112 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C4×C5×#10597243 |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7260 |
870 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 397);