Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D33⋊D25 |
| unambiguous semidirect product | D33⋊(C11×D25) |
| unambiguous semidirect product | D75⋊(C11×D11) |
| unambiguous semidirect product | D275⋊(D3×C11) |
| Fitting, Hall | C3×C112×C25 ⋊ C22 |
| derived | C3×C11×C25 ⋊ C22×C11 |
| Hall | C112×C25 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D25 |
| Sylow | C112 ⋊ D3×D25 |
| Hall | C3×C25 ⋊ C2×C11×D11 |
| Sylow | C25 ⋊ D3×C11×D11 |
| Sylow | C3 ⋊ C11×D11×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D33⋊D25 |
| commutator, cosocle, hypocenter | C3×C11×C25 | C22×C11 |
| Frattini | C5 | C11×D15⋊D11 |
| Fitting | C3×C112×C25 | C22 |
| socle | C3×C5×C112 | C2×D5 |
| LCS | G ▷ C3×C11×C25 | |
| UCS | C1 ◁ C11 | |
180 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
2607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 325);