Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#14559075⋊C5 |
| unambiguous semidirect product | #14559075⋊(C3×C5) |
| unambiguous semidirect product | (C3×#14559075)⋊C5 |
| Fitting, socle, Hall | C3×C112 ⋊ C5×Dic5 |
| derived | #10597245 ⋊ C3×C4×C5 |
| Hall | C3×C11⋊C52 ⋊ C4 |
| Hall | C11⋊C52 ⋊ C3×C4 |
| Sylow | C112 ⋊ C3×C5×Dic5 |
104 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 66 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 462);