Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#90379 |
| Fitting | C2×C7×#125 ⋊ C2 |
| Sylow | C7 ⋊ C2×#533 |
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13245275, #13319809, #13319928, … |
| maximal normal subgroup of | #13245275, #13319809, #13319928, … |
| maximal quotient of | C2×#11731593, C2×#11732383, C2×#11733408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17917);