Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×AGL(1,𝔽5)×C5⋊D5 |
| unambiguous semidirect product | D5⋊(C4×C5⋊D5) |
| Fitting, socle | C2×C53 ⋊ C2×C4 |
| derived, Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×C5⋊D5 |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×D5×C5⋊D5 | C2 |
| cosocle | C52×D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 939);