Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#463 ⋊ C2 |
| Sylow | C7 ⋊ #3040 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3040, C2×#11737980, #14220664, … |
| maximal normal subgroup of | D7×#3040, C2×#11737980, #14220664, … |
| maximal quotient of | #13337745, #13337754, #13337763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12746);