Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×#10620270 |
| derived, Sylow | C41 ⋊ C3×C16 |
| Hall | C3×C41 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #4223 |
| commutator, hypocenter | C41 | C3×C16 |
| Frattini | C4 | C3×#4223 |
| Fitting | C3×C4×C41 | C4 |
| socle, prime radical | C2×C3×C41 | C8 |
| cosocle | #66491 | C2×C3 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 1968 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 5);