Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013749 |
| derived | C3×C19×C49 ⋊ C3×C4 |
| Hall | C3×#14584108 ⋊ C4 |
| Hall | C19×C49 ⋊ C3×Dic3 |
| Sylow | C49 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ C3⋊((C49⋊C3)⋊C4) |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 11172 |
A minimal faithful permutation representation — 2 generators on 75 points:
(2,3)(4,5,6,7)(9,10,12)(11,14,18)(13,16,15)(17,21,22)(19,23,20)(24,26,25)(28,36,38,30,31,39)(29,48,50,34,35,51)(32,60,47,41,42,69)(33,65,66,45,46,75)(37,44,43,49,54,62)(40,63,72,58,59,73)(52,64,67,70,53,56)(55,68,57,71,61,74);(1,2,3)(8,9,11,14,19,24,23,12,15,20,21,10,13,17,18,22,25,26,16)(27,72,44,67,66,53,55,34,70,32,57,62,36,37,48,47,68,39,59,58,30,50,33,46,60,42,65,45,51,28,40,63,38,61,69,35,49,31,43,74,41,52,29,71,64,75,56,54,73)Polycyclic presentation:
2,3^2,7,19,2,7|a^2=f,d^7=g^6,c^a=c^2,d^a=d^6g,g^a=g^6,d^b=d^2g^3,e^b=e^11,g^b=g^2966 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 100);