Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | D5×2−1+4⋊C5 |
| unambiguous semidirect product | C5⋊(C2×2−1+4⋊C5) |
| unambiguous semidirect product | (D5×2−1+4)⋊C5 |
| Fitting, derived | C5×2−1+4 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C24⋊C5 |
| commutator, Fitting, cosocle, hypocenter | C5×2−1+4 | C2×C5 |
| socle | C2×C5 | C2×C24⋊C5 |
| LCS | G ▷ C5×2−1+4 | |
| UCS | C1 ◁ C2 | |
190 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9876);