Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×AGL(1,𝔽5)2 |
| unambiguous semidirect product | (D5×AGL(1,𝔽5))⋊(C2×C4) |
| Fitting, socle | C22×C52 ⋊ C42 |
| derived, Sylow | C52 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C22×C42 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52 | C42 |
| prime radical | C22×D52 | C22 |
| cosocle | D52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
1023 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 1023 conjugacy classes of subgroups — too many to draw. Only its 308 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10262);