Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#486 ⋊ C2 |
| Sylow | C7 ⋊ #3136 |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^d=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3136, C2×#11739008, #14223050, … |
| maximal normal subgroup of | D7×#3136, C2×#11739008, #14223050, … |
| maximal quotient of | #13353999, #13356443, #13356459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 13774);