Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#3874 |
| Fitting, socle | C22×C3×C52 ⋊ D3 |
| derived | C52⋊C3 ⋊ C23×C3 |
| Hall | C3×C52⋊C3 ⋊ C23 |
| Sylow | C52 ⋊ C22×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C22×C3 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 682);