Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D31×#568 |
| Fitting | C31×#568 ⋊ C2 |
| Sylow | C31 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D31 |
| commutator, socle | C2×C31 | C24×C4 |
| Fitting | C31×#568 | C2 |
| prime radical | C2×#41×D31 | C2 |
| cosocle | C4×C31 | C25 |
| hypercenter | #568 | D31 |
| hypocenter | C31 | C2×#568 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
578 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 19217);