Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×D52⋊C2 |
| unambiguous semidirect product | D52⋊(C22×C5) |
| Fitting, socle | C2×C53 ⋊ D4 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D52⋊C2 |
| commutator, cosocle | C5⋊D5 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | D4 |
| hypocenter | C52 | C2×C5×D4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2×C5 | |
232 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 941);