Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C7×#41 ⋊ C2 |
| Sylow | C7 ⋊ #3115 |
430 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^6,d^c=dg,f^c=fg152 conjugacy classes — view the full character table.
| maximal subgroup of | #13249603, #13249605, #13249610, … |
| maximal normal subgroup of | #13249603, #13249605, #13249610, … |
| maximal quotient of | #13353879, #13356827, #13356857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14742);