Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×AGL(1,𝔽5)2 |
| Fitting, socle, Hall | C3×C52 ⋊ C42 |
| derived, Sylow | C52 ⋊ C3×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C3×C42 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C42 |
| prime radical | C3×D52 | C22 |
| cosocle | D52 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 952);