Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3400 |
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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=g,b^2=e,c^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^6,f^c=fg,h^c=h^686 conjugacy classes — view the full character table.
| maximal subgroup of | #13344666, #13344668, #13344681, … |
| maximal normal subgroup of | #13344666, #13344668, #13344681, … |
| maximal quotient of | #13370642, #13370658, #13372660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12591);