Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#419 ⋊ C2 |
| Sylow | C7 ⋊ #2896 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eg,h^b=h^6,h^d=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | #13353142, #13355298, #13355307, … |
| maximal normal subgroup of | #13353142, #13355298, #13355307, … |
| maximal quotient of | #13320170, #13320230, #13320249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11167);