Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#19153449⋊C2)⋊C3 |
| unambiguous semidirect product | (#19153449⋊C3)⋊C2 |
| Fitting, socle, Sylow | C312 ⋊ C2×C3×D3 |
| derived | #15668333 ⋊ C22×C3 |
| Hall | C31⋊C32 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #15668333 | C22×C3 |
| Fitting, socle | C312 | C2×C3×D3 |
| LCS | G ▷ #15668333 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 62 |
A minimal faithful permutation representation — 2 generators on 62 points:
(1,2,3,10,11,12)(4,28,29,25,26,5)(6,15,14,23,30,8)(7,17,9,24,38,46)(13,52,53,47,48,18)(16,34,33,41,50,43)(19,36,49,45,54,21)(20,37,22,31,56,55)(27,62,61,44,32,39)(35,42,40,58,57,60)(51,59);(3,15,7,5,8,11)(4,17,14,10,12,6)(9,34,20,18,21,25)(13,37,33,24,26,19)(16,32,49,29,30,46)(22,56,41,39,42,47)(23,28,36,44,43,38)(27,50,55,31,48,40)(35,51,57,53,54,61)(45,52,58,59,60,62)Polycyclic presentation:
2^2,3^2,31^2|e^a=e^30,f^a=f^30,d^b=d^2,e^b=f^26,f^b=e^6,e^c=e^25,f^c=f^25,e^d=e^5,f^d=f^2573 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 135);