Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#338 ⋊ C2 |
| Sylow | C7 ⋊ #1813 |
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^b=h^6,f^c=fg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13264796, #13264800, #13264804, … |
| maximal normal subgroup of | #13264796, #13264800, #13264804, … |
| maximal quotient of | #13246656, #13246660, #13246664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1244);