Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of (C24⋊C25)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | C2×(C24⋊C25)⋊C2 |
| unambiguous semidirect product | (C24⋊C25)⋊C22 |
| unambiguous semidirect product | (C2×C24⋊C25)⋊C2 |
| derived | C24⋊C25 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C24⋊C25)⋊C2 |
| commutator, cosocle, hypocenter | C24⋊C25 | C22 |
| Frattini | C5 | C2×(C24⋊C5)⋊C2 |
| Fitting, socle | C25×C5 | D5 |
| LCS | G ▷ C24⋊C25 | |
| UCS | C1 ◁ C2 | |
376 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 376 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) = 50 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5601);