Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1534 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^6,d^b=dg,e^b=efg110 conjugacy classes — view the full character table.
| maximal subgroup of | #13246326, #13246329, #13246331, … |
| maximal normal subgroup of | #13246326, #13246329, #13246331, … |
| maximal quotient of | #13241876, #13241914, #13242076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4256);