Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2164 |
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^b=cg,h^c=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2164, C2×#11726848, #13506879, … |
| maximal normal subgroup of | D7×#2164, C2×#11726848, #13506879, … |
| maximal quotient of | #13268799, #13268833, #13269108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1614);