Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #1733 |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^6,c^b=cg164 conjugacy classes — view the full character table.
| maximal subgroup of | #13259114, #13259115, #13259119, … |
| maximal normal subgroup of | #13259114, #13259115, #13259119, … |
| maximal quotient of | #13243235, #13243241, #13243244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4098);