Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#13089712 |
| derived, Hall | C112⋊C3 ⋊ C4×C52 |
| Hall | C52×C112⋊C3 ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Sylow | C112 ⋊ C52×Dic3 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3300 |
1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 417);