Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26015421 |
| Fitting, socle, derived | C3×C31×C61 ⋊ C2×C3 |
| Hall | C3×#19150898 ⋊ C2 |
| Hall | C31×C61 ⋊ C3×D3 |
| Sylow | C61 ⋊ D3×C31⋊C3 |
| Sylow | C31 ⋊ C3⋊(D61⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C61 | C2×C3 |
| LCS | G ▷ C3×C31×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 5673 |
A minimal faithful permutation representation — 2 generators on 95 points:
(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,24)(14,18,21)(16,22,19)(20,27,30)(23,29,28)(25,31,26)(32,34,33)(36,40,41,37,38,42)(39,48,49,43,44,58)(45,61,62,51,52,74)(46,60,56,54,50,47)(53,79,80,64,65,90)(55,77,78,66,63,71)(57,59,76,68,69,72)(67,92,93,82,81,88)(70,75,91,84,83,89)(73,95,94,86,87,85);(1,2,3)(4,5,7,11,18,6,9,14,20,27,10,16,23,24,30,17,25,32,31,15,21,28,33,34,22,8,12,19,26,29,13)(35,36,39,45,53,65,81,87,89,90,84,68,56,41,40,46,55,67,83,52,63,72,74,88,94,78,49,60,48,59,73,86,69,44,50,58,71,85,93,62,76,77,61,75,82,66,54,38,42,47,57,70,80,91,95,92,79,64,51,43,37)Polycyclic presentation:
2,3^2,31,61|c^a=c^2,e^a=e^60,d^b=d^5,e^b=e^47969 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 52);