Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1376 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^a=h^6248 conjugacy classes — view the full character table.
| maximal subgroup of | #13240549, #13240550, #13240551, … |
| maximal normal subgroup of | #13240549, #13240550, #13240551, … |
| maximal quotient of | #13240628, #13240640, #13240647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 230);