Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11716856 |
| Sylow | C52 ⋊ C2×#100 |
439 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 439 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
142 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13103828, #72221701, #72221706 |
| maximal normal subgroup of | C2×#13103828, #72221701, #72221706 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7037);