Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013943 |
| Fitting, socle, derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×#14584116 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ C3⋊(#5997⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C19 | C3×C4 |
| prime radical | C3×#19150287 | C2 |
| cosocle | C3×C19×C7⋊D7 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 798 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,3)(4,5)(6,14,17,8,10,13,11,15,12,9,16,7)(19,20,22)(21,24,28)(23,26,25)(27,31,32)(29,33,30)(34,36,35);(1,2,3)(4,6,10,17,12,16,11)(5,13,9,15,14,8,7)(18,19,21,24,29,34,33,22,25,30,31,20,23,27,28,32,35,36,26)Polycyclic presentation:
2,3,2,3,7^2,19|a^2=c,d^a=d^2,e^a=e^4f^4,f^a=ef^3,e^b=e^2,f^b=f^2,g^b=g^11,e^c=e^6,f^c=f^6282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1073);