Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | (C19⋊C3)⋊#10596885 |
| Fitting, socle, Hall | C72×C19 ⋊ C3×Dic3 |
| derived | C19×#3862 ⋊ C3×C4 |
| Hall | C19⋊C3×#3862 ⋊ C4 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×#10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C19×#3862 | C3×C4 |
| Fitting, socle | C72×C19 | C3×Dic3 |
| prime radical | C19⋊C3×#64425 | C2 |
| cosocle | C19×#64425 | C2×C3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 266 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,5,8,6)(2,3)(4,14,10,13)(7,12,9,11)(16,20,21,17,18,22)(19,28,25,23,24,30)(26,31,33,32,29,27);(3,8,14)(4,11,6)(5,10,12)(7,13,9)(15,16,19,25,31,28,32,18,22,27,33,21,20,26,24,29,30,23,17)Polycyclic presentation:
2,3,2,3,19,7^2|a^2=c,d^a=d^2,e^a=e^18,f^a=f^3g^4,g^a=fg^4,e^b=e^7,f^c=f^6,g^c=g^6,f^d=f^2g^6,g^d=g^472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 778);