Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#89829 |
| Fitting | C2×C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ C2×#463 |
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13250128, #13250134, C4×#89829, … |
| maximal normal subgroup of | #13250128, #13250134, C4×#89829, … |
| maximal quotient of | C2×#11728954, C2×#11728986, C2×#11728955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15155);