Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#90768 |
| derived, Hall | C3×C29 ⋊ C16 |
| Sylow | C29 ⋊ C3⋊C16 |
| Sylow | C3 ⋊ #90768 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D87 |
| commutator, hypocenter | C3×C29 | C16 |
| Fitting, cosocle | C3×C8×C29 | C2 |
| socle, prime radical | C2×C3×C29 | C8 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 1392 |
Polycyclic presentation:
2^4,3,29|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^28360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 3);