Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1458 |
264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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=e,c^2=f,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | #13262879, #13262881, #13262887, … |
| maximal normal subgroup of | #13262879, #13262881, #13262887, … |
| maximal quotient of | #13241732, #13241740, #13241787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 620);