Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #87735 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#1035 |
| unambiguous semidirect product | D25⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#1035)⋊C23 |
| Fitting | C24×C25 ⋊ C4 |
| Sylow | C25 ⋊ C22×C22⋊C4 |
1011 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2033);