Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#533 ⋊ C2 |
| Sylow | C7 ⋊ #3076 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | #13248666, #13248672, #13248673, … |
| maximal normal subgroup of | #13248666, #13248672, #13248673, … |
| maximal quotient of | #13353264, #13354742, #13355953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15560);