Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of D3×C13⋊C3 |
| automorphism | Aut(G) = C2×D3×AGL(1,𝔽13) (order 1872) · Inn(G) = D3×C13⋊C3 · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C13⋊C3 |
| unambiguous semidirect product | C3⋊(C22×C13⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C13⋊C3) |
| unambiguous semidirect product | (C2×D3×C13)⋊C3 |
| Fitting, socle | C2×C3×C13 ⋊ C2×C3 |
| derived | C3×C13 ⋊ C22×C3 |
| Hall | C3×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C13⋊C3 |
| commutator, cosocle, hypocenter | C3×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 78 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2)(4,5)(7,8,10)(9,12,15)(11,14,13)(16,18,17);(1,2)(3,4,5)(6,7,9,8,11,15,12,16,18,10,13,17,14)42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic13⋊C3, #64602⋊C3, #64604⋊C3, … |
| maximal normal subgroup of | D3×Dic13⋊C3, #64602⋊C3, #64604⋊C3, … |
| maximal quotient of | Dic6×C13⋊C3, C4×D3×C13⋊C3, D12×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 34);