Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of A4×#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | A4×#4223 |
| unambiguous semidirect product | (C22×#4223)⋊C3 |
| Fitting, socle, derived | C22×C41 ⋊ C3×C4 |
| Hall | C22×#4223 ⋊ C3 |
| Sylow | C41 ⋊ C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C41 | C3×C4 |
| prime radical | A4×D41 | C2 |
| cosocle | C22×D41 | C2×C3 |
| LCS | G ▷ C22×C41 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 164 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#4223⋊C5, A4×#66502, S4×#4223 |
| maximal normal subgroup of | A4×#4223⋊C5, A4×#66502, S4×#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 187);