Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×#1035 |
| Fitting | #41×C25 ⋊ C4 |
| Sylow | C25 ⋊ C4×#41 |
465 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×#1035, AGL(1,ℤ/8)×#1035, #104×#1035, … |
| maximal normal subgroup of | H(5,𝔽2)×#1035, AGL(1,ℤ/8)×#1035, #104×#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2029);