Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#16838652⋊C3) |
| unambiguous semidirect product | (C3⋊#16838652)⋊C3 |
| Fitting, socle, derived | C3×C312 ⋊ C3×C4 |
| Hall | C3×#15668332 ⋊ C4 |
| Sylow | C312 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C312 | C3×C4 |
| prime radical | C3×#19153443 | C2 |
| cosocle | C3×C31⋊D31 | C2×C3 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 | |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 186 |
A minimal faithful permutation representation — 2 generators on 65 points:
(2,3)(4,5)(6,22,28,23,10,37,11,49,26,9,27,16)(7,33,36,34,14,39,15,60,17,13,35,32)(8,12,44,41,19,30,20,31,43,18,29,58)(21,59,50,42,47,56,48,57,40,46,54,65)(24,63,45,61,52,62,53,55,38,51,25,64);(1,2,3)(4,6,12,32,59,26,27,56,64,55,18,42,58,34,61,60,33,51,13,30,46,41,63,62,65,10,28,57,39,31,11)(5,45,14,50,23,25,24,49,19,8,7,37,36,48,43,54,47,44,21,17,16,15,20,29,22,53,52,9,40,35,38)Polycyclic presentation:
2,3,2,3,31^2|a^2=c,d^a=d^2,e^a=e^18f^14,f^a=e^10f^13,e^b=e^25,f^b=f^25,e^c=e^30,f^c=f^30258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 148);