Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #1820 |
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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,b^2=g,c^2=d,b^a=bd,c^a=ce,e^a=eg,h^b=h^6,f^c=fg98 conjugacy classes — view the full character table.
| maximal subgroup of | #13264458, #13264460, #13264468, … |
| maximal normal subgroup of | #13264458, #13264460, #13264468, … |
| maximal quotient of | #13247121, #13247127, #13247133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1473);