Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of D9 |
| automorphism | Aut(G) = C2×C3×C4×AGL(1,ℤ/9) (order 1296) · Inn(G) = D9 · Out(G) = C2×C32×C4 |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic9 |
| unambiguous semidirect product | C9⋊(C4×C13) |
| derived, Sylow | C9 ⋊ C4×C13 |
| Hall | C9×C13 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D9 |
| commutator, hypocenter | C9 | C4×C13 |
| Frattini | C2×C3 | D3×C13 |
| Fitting | C2×C9×C13 | C2 |
| socle, prime radical | C2×C3×C13 | D3 |
| cosocle | C2×C9 | C2×C13 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C13 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 468 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4)(6,8)(7,11)(9,10)(12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26);(5,13,8,11,10,9,7,6,12)156 conjugacy classes — view the full character table.
| maximal subgroup of | #11745422, #11745424, D13×Dic9, … |
| maximal normal subgroup of | #11745422, #11745424, D13×Dic9, … |
| maximal quotient of | C13×C9⋊C8, C2×C13×Dic9, C13×Dic27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 3);