Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×ΓL(1,𝔽16) |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52 | C42 |
| prime radical, cosocle | C3×D52 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 | |
126 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 953);