Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#89760 |
| Fitting | C22×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#390 |
1360 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13259157, #13260057, #13260067, … |
| maximal normal subgroup of | #13259157, #13260057, #13260067, … |
| maximal quotient of | C2×#11729317, C2×#11727162, C4×#89760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14364);