Finite Group DatabasebetaFinite Group Databasebeta| order | 19648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C307 ⋊ C2 |
| Sylow | C307 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9824 |
Polycyclic presentation:
2^6,307|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^306,c^b=cf,d^b=df,g^b=g^3063088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19648, 334);