Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#89834 |
| Fitting | C2×C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #13271136, #13271138, #13271146, … |
| maximal normal subgroup of | #13271136, #13271138, #13271146, … |
| maximal quotient of | C2×#11727456, C2×#11727471, C2×#11727457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15162);