Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#11716596 |
| Sylow | C52 ⋊ C2×#97 |
400 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13100501, C22×#11716596, #72242678, … |
| maximal normal subgroup of | C2×#13100501, C22×#11716596, #72242678, … |
| maximal quotient of | C22×#11716596 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3608);