Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C349 ⋊ C2 |
| Sylow | C349 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11168 |
Polycyclic presentation:
2^6,349|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^348,c^b=cf,d^b=df,g^b=g^3483508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 334);