Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#87877 |
| Fitting | C42×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×C4×D4 |
960 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 960 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) = 160 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #72220757, #72220789, C4×#11717363, … |
| maximal normal subgroup of | #72220757, #72220789, C4×#11717363, … |
| maximal quotient of | #72220721, #72220903, #72223028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7438);