Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2161 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^6,c^b=cg152 conjugacy classes — view the full character table.
| maximal subgroup of | #13269223, #13269228, #13270323, … |
| maximal normal subgroup of | #13269223, #13269228, #13270323, … |
| maximal quotient of | #13265385, #13265449, #13265477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3949);