Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C31×#568 ⋊ C2 |
| Sylow | C31 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D31 |
| commutator, socle | C2×C31 | C24×C4 |
| Fitting | C31×#568 | C2 |
| prime radical | #14521885 | C2 |
| cosocle | C4×C31 | C25 |
| hypercenter | #568 | D31 |
| hypocenter | C31 | #3573 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^7,31|a^2=f,f^2=g,h^a=h^30,e^b=eg,d^c=dg,h^e=h^30578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 19223);