Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26015425 |
| Fitting, socle, derived | C3×C31×C61 ⋊ C2×C3 |
| Hall | C3×#19150898 ⋊ C2 |
| Hall | C31×C61 ⋊ C3×D3 |
| Sylow | C61 ⋊ C3⋊(D31⋊C3) |
| Sylow | C31 ⋊ D3×C61⋊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)(5,9,10,6,7,11)(8,17,18,12,13,25)(14,28,29,20,21,33)(15,27,23,22,19,16)(24,26,34,30,31,32)(36,37,39)(38,41,46)(40,44,43)(42,48,56)(45,51,53)(47,54,50)(49,58,68)(52,60,65)(55,63,62)(57,66,59)(61,71,78)(64,73,75)(67,76,72)(69,79,70)(74,82,86)(77,84,83)(80,87,81)(85,90,91)(88,92,89)(93,95,94);(1,2,3)(4,5,8,14,22,7,11,16,24,31,13,19,25,29,34,21,28,32,33,18,27,17,26,30,23,10,9,15,20,12,6)(35,36,38,42,49,58,69,80,88,93,92,76,54,39,43,50,59,70,71,48,57,67,77,85,87,66,46,53,62,72,81,82,60,41,47,55,64,74,79,56,65,75,83,89,90,73,51,37,40,45,52,61,68,78,86,91,94,95,84,63,44)Polycyclic presentation:
2,3^2,31,61|c^a=c^2,d^a=d^30,d^b=d^5,e^b=e^47984 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 48);