Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of A4⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊#4223 |
| Fitting, socle | C22×C41 ⋊ Dic3 |
| derived | A4×C41 ⋊ C4 |
| Sylow | C41 ⋊ SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | A4×C41 | C4 |
| Fitting, socle | C22×C41 | Dic3 |
| prime radical, cosocle | A4×D41 | C2 |
| LCS | G ▷ A4×C41 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 164 |
Polycyclic presentation:
2^2,3,41,2^2|a^2=b,c^a=c^2,d^a=d^32,e^a=ef,d^b=d^40,e^c=f,f^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #72254112, S4×#4223 |
| maximal normal subgroup of | #72254112, S4×#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 186);