Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of D13 |
| automorphism | Aut(G) = C22×C3×AGL(1,𝔽13) (order 1872) · Inn(G) = D13 · Out(G) = C23×C32 |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D13 |
| Fitting | C2×C9×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C22×C9 |
| Hall | C9×C13 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D13 |
| commutator, hypocenter | C13 | C22×C9 |
| Frattini | C3 | C2×C3×D13 |
| Fitting | C2×C9×C13 | C2 |
| socle | C2×C3×C13 | C2×C3 |
| prime radical | C2×C3×D13 | C3 |
| cosocle | C3×C13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 234 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2)(3,7,11,5,10,6,8,4,9)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);(1,2)(12,13,15,17,19,21,23,24,22,20,18,16,14)144 conjugacy classes — view the full character table.
| maximal subgroup of | D13×Dic9, #11745427, #11745428, … |
| maximal normal subgroup of | D13×Dic9, #11745427, #11745428, … |
| maximal quotient of | C9×Dic26, C4×C9×D13, C9×D52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 15);