Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#452 ⋊ C2 |
| Sylow | C7 ⋊ #3007 |
754 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^6,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3007, C2×#11737673, #14220184, … |
| maximal normal subgroup of | D7×#3007, C2×#11737673, #14220184, … |
| maximal quotient of | #13326196, #13326235, #13326274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12439);