Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#367 ⋊ C2 |
| Sylow | C7 ⋊ #2177 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^6,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13274418, #13274420, D7×#2177, … |
| maximal normal subgroup of | #13274418, #13274420, D7×#2177, … |
| maximal quotient of | #13265546, #13265718, #13265803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1859);