Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C72×C19 ⋊ C22×C3 |
| Hall | C3×#14584116 ⋊ C22 |
| Hall | C72×C19 ⋊ C2×C3×D3 |
| Sylow | C72 ⋊ C2×D3×C19⋊C3 |
| Sylow | C19 ⋊ #13183634 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
248 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 798 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,3)(4,5,6,10,7,9)(11,12,17)(14,15,16)(19,20,22)(21,24,28)(23,26,25)(27,31,32)(29,33,30)(34,36,35);(1,2,3)(5,6)(7,8)(9,10)(12,13)(14,15)(16,17)(18,19,21,24,29,34,33,22,25,30,31,20,23,27,28,32,35,36,26)Polycyclic presentation:
2^2,3^2,7^2,19|e^a=e^6,f^a=f^6,d^b=d^2,e^b=e^6,e^c=e^2,f^c=f^2,g^c=g^11339 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1230);