Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×D11×C11⋊C25 |
| derived, Hall | C3×C112 ⋊ C22×C25 |
| Hall | C3×C11×C11⋊C25 ⋊ C22 |
| Hall | C11×C11⋊C25 ⋊ C2×D3 |
| Hall | D3×C11×D11 ⋊ C25 |
| Sylow | C112 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×D11×C11⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D3×D11×C11⋊C5 |
| commutator, hypocenter | C3×C112 | C22×C25 |
| Fitting, socle, cosocle | C3×C5×C112 | C22×C5 |
| prime radical | C5×D3×C11×D11 | C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 236);