Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2921 |
392 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 392 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) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^6,c^b=cg164 conjugacy classes — view the full character table.
| maximal subgroup of | #13247825, #13247829, #13248888, … |
| maximal normal subgroup of | #13247825, #13247829, #13248888, … |
| maximal quotient of | #13351276, #13351343, #13351703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14420);