Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D52⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D52⋊D3 |
| unambiguous semidirect product | D52⋊(C3×D3) |
| Fitting, socle, Hall | C32×C52 ⋊ D4 |
| Sylow | C52 ⋊ C3×#67 |
| Sylow | C32 ⋊ D52⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D52⋊D3 |
| commutator, cosocle | C3×C5⋊D5 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | D4 |
| hypocenter | C3×C52 | C3×D4 |
| LCS | G ▷ C3×C5⋊D5 ▷ C3×C52 | |
| UCS | C1 ◁ C3 | |
140 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 652);