Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11716850 |
| unambiguous semidirect product | D5⋊#3964 |
| Fitting | C2×C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ C2×#102 |
431 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7008);