Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C121 · Schur multiplier (H2) = C2 |
| direct product | D5×D15×C121 |
| unambiguous semidirect product | (C3×D5)⋊(D5×C121) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C121) |
| Fitting, Hall | C3×C52×C121 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C121 |
| Hall | C52×C121 ⋊ C2×D3 |
| Hall | C3×C121 ⋊ D52 |
| Sylow | C52 ⋊ C2×D3×C121 |
| Sylow | C3 ⋊ D52×C121 |
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3630 |
4356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 132);