Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of C22⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C13⋊C9) |
| unambiguous semidirect product | C13⋊(C22⋊C9) |
| derived, Hall | C22×C13 ⋊ C9 |
| Sylow | C13 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C13⋊C3) |
| commutator, hypocenter | C22×C13 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C13 | C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 234 |
A minimal faithful permutation representation — 2 generators on 26 points:
(2,3,4)(5,6,8,7,9,11,10,12,13)(15,16,18)(17,20,23)(19,22,21)(24,26,25);(1,4)(2,3)(14,15,17,16,19,23,20,24,26,18,21,25,22)Polycyclic presentation:
3^2,2^2,13|a^3=b,c^a=d,d^a=cd,e^a=e^360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 14);