Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #3209 |
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^6,f^c=fg89 conjugacy classes — view the full character table.
| maximal subgroup of | #13327784, #13327786, #13327800, … |
| maximal normal subgroup of | #13327784, #13327786, #13327800, … |
| maximal quotient of | #13363105, #13363475, #13364314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12389);