Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1987 |
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=deg,c^2=ef,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cef,h^a=h^6,d^b=dg,e^b=eg,f^b=fg158 conjugacy classes — view the full character table.
| maximal subgroup of | #13245717, #13245722, #13245731, … |
| maximal normal subgroup of | #13245717, #13245722, #13245731, … |
| maximal quotient of | #13253777, #13253795, #13253913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2009);