Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| isoclinism | isoclinic class of C3⋊(D13⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(Dic13⋊A4) |
| unambiguous semidirect product | Dic39⋊A4 |
| derived | C22×C3×C13 ⋊ C3×C4 |
| Sylow | C13 ⋊ Dic3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D13⋊A4) |
| commutator, hypocenter | C22×C3×C13 | C3×C4 |
| Fitting, socle, cosocle | C23×C3×C13 | C2×C3 |
| prime radical | C2×C3×C22⋊(C13⋊C3) | C2 |
| LCS | G ▷ C22×C3×C13 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2,3,2^3,3,13|a^2=c,f^a=f^2,g^a=g^12,d^b=de,e^b=d,g^b=g^372 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 781);