Finite Group DatabasebetaFinite Group Databasebeta| order | 4290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C13⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C13⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊D39 |
| unambiguous semidirect product | D429⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C13 | C2×C5 |
| LCS | G ▷ C3×C11×C13 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 429 |
Polycyclic presentation:
2,3,5,11,13|b^a=b^2,d^a=d^10,e^a=e^12,d^c=d^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4290, 26);