Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#467 ⋊ C2 |
| Sylow | C7 ⋊ #3059 |
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^d=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13507628, #13507630, #13507646, … |
| maximal normal subgroup of | #13507628, #13507630, #13507646, … |
| maximal quotient of | #13336869, #13336908, #13336958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12971);