Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#66082 |
| Fitting | C2×C52×M16 ⋊ C2 |
| Sylow | C52 ⋊ #575 |
592 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72220946, C5×#10619093, #72221389, … |
| maximal normal subgroup of | #72220946, C5×#10619093, #72221389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9254);