Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of C3⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3⋊#4223 |
| unambiguous semidirect product | D41⋊(C2×Dic3) |
| Fitting, socle | C22×C3×C41 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C22×C4 |
| Sylow | C41 ⋊ C22×Dic3 |
| Sylow | C3 ⋊ C22×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C41 | C4 |
| prime radical | C22×C3×D41 | C2 |
| cosocle | C3×D41 | C23 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 492 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 196);