Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×#4223 |
| Fitting | C3×C4×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C3×C42 |
| Hall | C3×C41 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #4223 |
| commutator, hypocenter | C41 | C3×C42 |
| Frattini | C2 | C2×C3×#4223 |
| Fitting | C3×C4×C41 | C4 |
| socle | C2×C3×C41 | C2×C4 |
| prime radical | C2×C3×D41 | C22 |
| cosocle | C2×D41 | C22×C3 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 492 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 109);