Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#346 ⋊ C2 |
| Sylow | C7 ⋊ #1330 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^6,c^b=ceg,d^b=dg,h^b=h^6158 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1330, C2×#11725321, #13263513, … |
| maximal normal subgroup of | D7×#1330, C2×#11725321, #13263513, … |
| maximal quotient of | #13240458, #13240461, #13240464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 87);