Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C283 ⋊ C2 |
| Sylow | C283 ⋊ #3006 |
806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^7,283|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^2823134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 13758);