Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #3012 |
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^6,d^c=dg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13385247, #13385250, #13385265, … |
| maximal normal subgroup of | #13385247, #13385250, #13385265, … |
| maximal quotient of | #13326999, #13327032, #13327087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16160);