Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#367 ⋊ C2 |
| Sylow | C7 ⋊ #2158 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^b=h^6,h^c=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | #13274257, #13274315, D7×#2158, … |
| maximal normal subgroup of | #13274257, #13274315, D7×#2158, … |
| maximal quotient of | #13265380, #13265444, #13265485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1865);