Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #1331 |
110 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 49 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=d,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^6,c^b=ce,e^b=eg128 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1331, C2×#11725569, #13263533, … |
| maximal normal subgroup of | D7×#1331, C2×#11725569, #13263533, … |
| maximal quotient of | #13240445, #13240457, #13240563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 335);