Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#89462 |
| Fitting | C2×C4×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#433 |
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #13244333, #13244335, #13246662, … |
| maximal normal subgroup of | #13244333, #13244335, #13246662, … |
| maximal quotient of | C2×#11727505, C2×#11727507, C2×#11727509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10665);