Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C31 ⋊ C2 |
| Sylow | C31 ⋊ #3364 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^7,31|b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^30,d^b=de,f^c=fg,h^d=h^30455 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 17196);