Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #2401 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^7,31|a^2=fg,b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^30,h^c=h^30644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 7811);