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) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C13⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C13⋊C3) |
| unambiguous semidirect product | (Dic3×C13)⋊C3 |
| derived | C3×C13 ⋊ C3×C4 |
| Hall | C3×C13⋊C3 ⋊ C4 |
| Sylow | C13 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C13⋊C3 |
| commutator, hypocenter | C3×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C13 | C2×C3 |
| prime radical | C2×C3×C13⋊C3 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 156 |
A minimal faithful permutation representation — 2 generators on 20 points:
(2,3)(4,5,6,7)(9,10,12)(11,14,17)(13,16,15)(18,20,19);(1,2,3)(8,9,11,10,13,17,14,18,20,12,15,19,16)42 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D13⋊C3, #64601⋊C3, #64603⋊C3, … |
| maximal normal subgroup of | Dic3×D13⋊C3, #64601⋊C3, #64603⋊C3, … |
| maximal quotient of | C3⋊C8×C13⋊C3, C2×Dic3×C13⋊C3, Dic9×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 20);