Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #1832 |
216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 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=e,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^6,h^c=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | #13240437, #13247918, #13247919, … |
| maximal normal subgroup of | #13240437, #13247918, #13247919, … |
| maximal quotient of | #13247449, #13247453, #13247466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2964);