Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C2×C4×D5) |
| unambiguous semidirect product | (C5×AGL(1,𝔽5))⋊C23 |
| unambiguous semidirect product | #1042⋊C23 |
| Fitting, socle | C22×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52 | C2×C4 |
| prime radical | C22×D52 | C2 |
| cosocle | C5×D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
488 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1200);