Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1298 |
190 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 65 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=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^6,c^b=cg158 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1298, C2×#11725486, #13243937, … |
| maximal normal subgroup of | D7×#1298, C2×#11725486, #13243937, … |
| maximal quotient of | #13240350, #13240358, #13240359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 252);