Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C109 ⋊ #1569 |
166 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6976 |
Polycyclic presentation:
2^7,109|a^2=e,b^2=d,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^33,c^b=cf,h^b=h^108,h^c=h^108,h^e=h^108572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 20076);