Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×D5⋊#168 |
| unambiguous semidirect product | D5⋊(C5×#168) |
| derived | C52 ⋊ C2×C5×C8 |
| Sylow | C53 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #1042 |
| commutator, hypocenter | C52 | C2×C5×C8 |
| Frattini | C2 | C2×C5×#1042 |
| Fitting | C4×C53 | C4 |
| socle | C2×C53 | C2×C4 |
| prime radical | C2×C52×D5 | C4 |
| cosocle | C5×Dic5 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4×C5 | |
156 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 765);