Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11 |
| direct product | C3×C5×#14559097 |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C4 |
| derived | C5×C112 ⋊ C3×C4×C5 |
| Hall | C52×C112 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C112 ⋊ C3×C5×AGL(1,𝔽5) |
| Hall | C3×C52 ⋊ #92150 |
| Sylow | C52 ⋊ C3×#92150 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
2325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 849);