Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D52×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D52×AGL(1,𝔽5) |
| unambiguous semidirect product | (C5×D5×AGL(1,𝔽5))⋊C2 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C5⋊D5)⋊C2 |
| unambiguous semidirect product | (D5×#1042)⋊C2 |
| Fitting, socle, derived, Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C22×C4 |
| prime radical | D53 | C2 |
| cosocle | C52×D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
276 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 918);