Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#498 ⋊ C2 |
| Sylow | C7 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=dfg,e^2=f,f^2=g,b^a=bdfg,c^a=ce,e^a=ef,f^a=fg,d^c=dg,e^c=efg,f^c=fg,h^c=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | #13267553, #13267554, #13267558, … |
| maximal normal subgroup of | #13267553, #13267554, #13267558, … |
| maximal quotient of | #13269894, #13270492, #13271492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3870);