Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5×#10624391⋊C5 |
| unambiguous semidirect product | (C2×#10624391)⋊C52 |
| unambiguous semidirect product | (C2×C5×#10624391)⋊C5 |
| Fitting, socle | C2×C5×C112 ⋊ C5×D3 |
| derived, Hall | C112⋊C3 ⋊ C22×C52 |
| Hall | C5×(C112⋊C3)⋊C5 ⋊ C22 |
| Hall | C5×#10597243 ⋊ C2×D3 |
| Hall | C2×#10624391 ⋊ C52 |
| Sylow | C112 ⋊ C2×C52×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #10624391⋊C5 |
| commutator, cosocle, hypocenter | C112⋊C3 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C112 | C5×D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C2×C5 | |
256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 495);