Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C5×D52 |
| unambiguous semidirect product | (C5×D5)⋊(C23×C5) |
| Fitting, socle | C22×C53 ⋊ C22 |
| derived | C52 ⋊ C24×C5 |
| Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | D52 |
| commutator, cosocle, hypocenter | C52 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C5 | |
768 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 957);