Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#15667734 |
| Fitting | D4×C353 ⋊ C8 |
| Sylow | C353 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2824 |
Polycyclic presentation:
2^6,353|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^283,c^b=ce,g^d=g^311,g^f=g^352248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1636);