Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #2253 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=dg,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^6,h^c=h^6104 conjugacy classes — view the full character table.
| maximal subgroup of | #13274710, #13274711, D7×#2253, … |
| maximal normal subgroup of | #13274710, #13274711, D7×#2253, … |
| maximal quotient of | #13270236, #13271825, #13271829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1863);