Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #1373 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^b=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1373, C2×#11725372, #13265390, … |
| maximal normal subgroup of | D7×#1373, C2×#11725372, #13265390, … |
| maximal quotient of | #13240535, #13240537, #13240679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 138);