Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#87872 |
| Sylow | C52 ⋊ C23×Q8 |
1936 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 1936 conjugacy classes of subgroups — too many to draw. Only its 608 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11717477, C22×#11717353, C22×#11717355, … |
| maximal normal subgroup of | C22×#11717477, C22×#11717353, C22×#11717355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10157);