Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊#10596868 |
| derived | C19×#3862 ⋊ C3×C4 |
| Hall | C19⋊C3×#3862 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×#10596868 |
104 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 532 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4)(5,8,18,15,14,10,12,13,17,6,7,16,11,9)(20,24,25,21,22,26)(23,32,29,27,28,34)(30,35,37,36,33,31);(7,11,12)(8,13,10)(9,15,16)(14,18,17)(19,20,23,29,35,32,36,22,26,31,37,25,24,30,28,33,34,27,21)Polycyclic presentation:
2,3^2,19,7^2,2|a^2=g,c^a=c^2,d^a=d^18,e^a=e^2f^3,f^a=e^6f^5,d^b=d^7,e^c=e^4f^4,f^c=f^2234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 612);