Finite Group DatabasebetaFinite Group Databasebeta| order | 234 |
| isoclinism | isoclinic class of D3×C13⋊C3 |
| automorphism | Aut(G) = D3×AGL(1,𝔽13) (order 936) · Inn(G) = G · Out(G) = C4 |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D3×C13⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C13⋊C3) |
| unambiguous semidirect product | (D3×C13)⋊C3 |
| Fitting, socle, derived | C3×C13 ⋊ C2×C3 |
| Hall | C3×C13⋊C3 ⋊ C2 |
| Sylow | C13 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 39 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,3)(5,6,8)(7,10,13)(9,12,11)(14,16,15);(1,2,3)(4,5,7,6,9,13,10,14,16,8,11,15,12)21 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D13⋊C3, C2×D3×C13⋊C3, #10622031, … |
| maximal normal subgroup of | D3×D13⋊C3, C2×D3×C13⋊C3, C3×D3×C13⋊C3, … |
| maximal quotient of | Dic3×C13⋊C3, C2×D3×C13⋊C3, #10622031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(234, 8);