Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #2274 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^6188 conjugacy classes — view the full character table.
| maximal subgroup of | #13351593, #13351595, #13351597, … |
| maximal normal subgroup of | #13351593, #13351595, #13351597, … |
| maximal quotient of | #13274877, #13274880, #13274881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5961);