Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D11×C25×D33 |
| Fitting, Hall | C3×C112×C25 ⋊ C22 |
| derived, Hall | C3×C112 ⋊ C22×C25 |
| Hall | C112×C25 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×D3×C25 |
| Hall | C3×C25 ⋊ D112 |
| Sylow | C3 ⋊ D112×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D11×D33 |
| commutator, hypocenter | C3×C112 | C22×C25 |
| Frattini | C5 | C5×D11×D33 |
| Fitting | C3×C112×C25 | C22 |
| socle, cosocle | C3×C5×C112 | C22×C5 |
| prime radical | C5×D11×D33 | C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C25 | |
180 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 180 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) = 1650 |
3150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 310);