Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ #2875 |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^6,d^c=dg,h^c=h^6188 conjugacy classes — view the full character table.
| maximal subgroup of | #13268869, #13352374, #13352375, … |
| maximal normal subgroup of | #13268869, #13352374, #13352375, … |
| maximal quotient of | #13319388, #13319390, #13319407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10761);