Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D25 |
| Fitting | C25×#99 ⋊ C2 |
| Sylow | C25 ⋊ C2×#99 |
315 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#1035, D25×B(4,𝔽2), #72275694, … |
| maximal normal subgroup of | #99×#1035, D25×B(4,𝔽2), #72275694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 370);