Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C112 · Schur multiplier (H2) = C2×C11 |
| direct product | C5×D3×D5×C112 |
| unambiguous semidirect product | (C5×D3)⋊(C2×C5×C112) |
| unambiguous semidirect product | (C3×D5)⋊(C2×C5×C112) |
| unambiguous semidirect product | D15⋊(C2×C5×C112) |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C22 |
| derived | C3×C5 ⋊ C22×C5×C112 |
| Hall | C52×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×C5×D5 |
| Hall | C3×C52 ⋊ C22×C112 |
| Sylow | C52 ⋊ C2×D3×C112 |
| Sylow | C3 ⋊ C2×C5×D5×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C112 | D3×D5 |
| commutator, cosocle, hypocenter | C3×C5 | C22×C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C5×C112 | |
672 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3630 |
7260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 887);