Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of A4⋊D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊Dic29 |
| derived | A4×C29 ⋊ C4 |
| Sylow | C29 ⋊ SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4⋊D29 |
| commutator, hypocenter | A4×C29 | C4 |
| Fitting, socle | C23×C29 | D3 |
| prime radical, cosocle | C2×A4×C29 | C2 |
| LCS | G ▷ A4×C29 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 348 |
Polycyclic presentation:
2^2,3,29,2^2|a^2=b,c^a=c^2,d^a=d^28,e^a=ef,e^c=f,f^c=ef122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 101);