Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D15×C41 |
| unambiguous semidirect product | (C3×D5)⋊(C3×D5×C41) |
| unambiguous semidirect product | (C5×D5)⋊(C3×D3×C41) |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C22 |
| derived | C3×C52 ⋊ C22×C3×C41 |
| Hall | C52×C41 ⋊ C2×C3×D3 |
| Hall | C32×C41 ⋊ D52 |
| Hall | C32×C52 ⋊ C22×C41 |
| Sylow | C52 ⋊ C2×C3×D3×C41 |
| Sylow | C32 ⋊ D52×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D5×D15 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3×C41 | |
212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2460 |
4428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 522);