Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D552 |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C22 |
| derived, Hall | C52×C112 ⋊ C22×C3 |
| Hall | C3×C112 ⋊ D52 |
| Sylow | C112 ⋊ C3×D52 |
| Hall | C3×C52 ⋊ D112 |
| Sylow | C52 ⋊ C3×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D552 |
| commutator, cosocle, hypocenter | C52×C112 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C22 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C3 | |
352 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
2523 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 860);