Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #2165 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^6,e^b=eg,e^c=eg152 conjugacy classes — view the full character table.
| maximal subgroup of | #13240856, #13240857, #13240859, … |
| maximal normal subgroup of | #13240856, #13240857, #13240859, … |
| maximal quotient of | #13268812, #13268862, #13269130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2384);