Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of D3×#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×#4223 |
| unambiguous semidirect product | D41⋊(C4×D3) |
| unambiguous semidirect product | (C3×#4223)⋊C22 |
| unambiguous semidirect product | (C3⋊#4223)⋊C22 |
| unambiguous semidirect product | (D3×D41)⋊C4 |
| Fitting, socle | C2×C3×C41 ⋊ C2×C4 |
| derived, Hall | C3×C41 ⋊ C22×C4 |
| Sylow | C41 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C22×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#4223 |
| commutator, hypocenter | C3×C41 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C41 | C2×C4 |
| prime radical | C2×D3×D41 | C2 |
| cosocle | C3×D41 | C23 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 246 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#66502, C2×D3×#4223⋊C5, D32×#4223 |
| maximal normal subgroup of | C2×D3×#66502, C2×D3×#4223⋊C5 |
| maximal quotient of | D32×#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 191);