Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽13) |
| automorphism | Aut(G) = D3×AGL(1,𝔽13) (order 936) · Inn(G) = G · Out(G) = C2 |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊AGL(1,𝔽13) |
| unambiguous semidirect product | (C3⋊#261)⋊C3 |
| Fitting, socle, derived | C3×C13 ⋊ C3×C4 |
| Hall | C3×C13⋊C3 ⋊ C4 |
| Sylow | C13 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13 | C3×C4 |
| prime radical | C3×D13⋊C3 | C2 |
| cosocle | C3×D13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 | |
28 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)(5,10,14,11,7,15,8,16,12,6,13,9);(1,2,3)(4,5,9,12,13,11,16,10,6,7,14,15,8)Polycyclic presentation:
2,3,2,3,13|a^2=c,d^a=d^2,e^a=e^8,e^b=e^9,e^c=e^1221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 30);