Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ #2392 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^6,c^b=cg164 conjugacy classes — view the full character table.
| maximal subgroup of | #13359894, #13359895, #13359905, … |
| maximal normal subgroup of | #13359894, #13359895, #13359905, … |
| maximal quotient of | #13275478, #13275479, #13275499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14556);