Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#90422 |
| Fitting | C2×C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13246337, #13358950, #13359075, … |
| maximal normal subgroup of | #13246337, #13358950, #13359075, … |
| maximal quotient of | C2×#11731803, C2×#11733928, C2×#11734056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18042);