Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C7 ⋊ #1716 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^6,c^b=cf,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | #13267569, D7×#1716, C2×#11729092, … |
| maximal normal subgroup of | #13267569, D7×#1716, C2×#11729092, … |
| maximal quotient of | #13247578, #13253569, #13253583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3858);