Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×C22⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #3056 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13391233, #13391237, #13391255, … |
| maximal normal subgroup of | #13391233, #13391237, #13391255, … |
| maximal quotient of | #13336571, #13336593, #13336615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14943);