Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C7 ⋊ #2379 |
520 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 213 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,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^6,c^b=cef,d^b=de122 conjugacy classes — view the full character table.
| maximal subgroup of | #13248150, #13248153, #13248155, … |
| maximal normal subgroup of | #13248150, #13248153, #13248155, … |
| maximal quotient of | #13275420, #13275431, #13275438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15168);