Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#64867 |
| Sylow | C52 ⋊ #344 |
197 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72221646, C5×#10604463, #72221693, … |
| maximal normal subgroup of | #72221646, C5×#10604463, #72221693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2409);