Finite Group DatabasebetaFinite Group Databasebeta| order | 429 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | Aut(G) = C2×C5×AGL(1,𝔽13) (order 1560) · Inn(G) = C13⋊C3 · Out(G) = C2×C4×C5 |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C11) |
| unambiguous semidirect product | (C11×C13)⋊C3 |
| Fitting, socle, Hall | C11×C13 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 143 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14,16)(15,18,21)(17,20,19)(22,24,23);(12,13,15,14,17,21,18,22,24,16,19,23,20)77 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D13⋊C3, D11×C13⋊C3, C11⋊(D13⋊C3), … |
| maximal normal subgroup of | C11×D13⋊C3, D11×C13⋊C3, C11⋊(D13⋊C3), … |
| maximal quotient of | C2×C11×C13⋊C3, C11×C13⋊C9, C3×C11×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(429, 1);