Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #3036 |
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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|b^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^6,f^c=fg98 conjugacy classes — view the full character table.
| maximal subgroup of | #13388364, #13388368, #13388375, … |
| maximal normal subgroup of | #13388364, #13388368, #13388375, … |
| maximal quotient of | #13337571, #13337577, #13337582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16142);