Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×AGL(1,𝔽5)2 |
| unambiguous semidirect product | (D5×AGL(1,𝔽5))⋊C4 |
| Fitting, socle | C2×C52 ⋊ C42 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C42 |
| prime radical | C2×D52 | C22 |
| cosocle | D52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
224 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1192);