Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#1035 |
| Fitting | M16×C25 ⋊ C4 |
| Sylow | C25 ⋊ C4×M16 |
213 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 79 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 | #100×#1035, AGL(1,ℤ/8)×#1035, #104×#1035, … |
| maximal normal subgroup of | #100×#1035, AGL(1,ℤ/8)×#1035, #104×#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1068);