Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #26040341⋊C3 |
| derived | #15668333 ⋊ C3×C4 |
| Hall | C31⋊C32 ⋊ C4 |
| Sylow | C312 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19153449⋊C3 |
| commutator, hypocenter | #15668333 | C3×C4 |
| Fitting, socle | C2×C312 | C3×D3 |
| prime radical | C2×C31⋊C32 | C2 |
| cosocle | C2×#15668333 | C2×C3 |
| LCS | G ▷ #15668333 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 124 |
A minimal faithful permutation representation — 2 generators on 66 points:
(1,2,3,4)(5,16,13,30,11,14)(6,7,34,38,28,24)(8,32,29,64,49,45)(9,18,50,27,52,42)(10,26,25,56,22,47)(12,31,59,63,53,19)(15,61,55,66,33,54)(17,44,65,48,37,23)(20,36,46,40,57,60)(21,51,43,35,41,62)(39,58);(7,11,10)(8,14,26)(9,16,19)(12,22,21)(13,24,18)(15,28,46)(17,30,51)(20,34,37)(23,41,40)(25,42,36)(27,45,44)(29,49,62)(31,52,39)(32,38,53)(33,47,50)(35,56,57)(43,60,58)(48,54,59)(55,63,65)(61,64,66)Polycyclic presentation:
2,3^2,31^2,2|a^2=f,c^a=c^2,d^a=e^26,e^a=d^6,d^b=d^25,e^b=e^25,d^c=d^5,e^c=e^25208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 101);