Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26040337 |
| derived | C3×C312 ⋊ C3×C4 |
| Hall | C3×#15668332 ⋊ C4 |
| Sylow | C312 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19153445 |
| commutator, hypocenter | C3×C312 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C312 | C2×C3 |
| prime radical | C2×C3×#15668332 | C2 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 ◁ C2 | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 372 |
A minimal faithful permutation representation — 2 generators on 69 points:
(2,3)(4,5,6,7)(9,13,14,10,11,15)(12,21,22,16,17,29)(18,32,33,24,25,37)(19,31,27,26,23,20)(28,30,38,34,35,36)(40,41,43)(42,45,50)(44,48,47)(46,52,59)(49,53,56)(51,57,54)(55,62,65)(58,64,63)(60,66,61)(67,69,68);(1,2,3)(8,9,12,18,26,11,15,20,28,35,17,23,29,33,38,25,32,36,37,22,31,21,30,34,27,14,13,19,24,16,10)(39,40,42,46,53,41,44,49,55,62,45,51,58,59,65,52,60,67,66,50,56,63,68,69,57,43,47,54,61,64,48)Polycyclic presentation:
2,3^2,31^2,2|a^2=f,c^a=c^2,d^a=d^30,d^b=d^5,e^b=e^51008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 115);