Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C19×#3862 ⋊ C3×C4 |
| Hall | #22552728 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ #10596868⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30660728 |
| commutator, hypocenter | C19×#3862 | C3×C4 |
| Fitting, socle | C2×C72×C19 | C3×D3 |
| prime radical | C2×#22552728 | C2 |
| cosocle | C2×C19×#3862 | C2×C3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 19 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)(5,15,12,17,11,13)(6,7,9,16,8,18)(10,14)(20,21,23)(22,25,29)(24,27,26)(28,32,33)(30,34,31)(35,37,36);(7,11,10)(8,13,14)(9,15,17)(12,18,16)(19,20,22,25,30,35,34,23,26,31,32,21,24,28,29,33,36,37,27)Polycyclic presentation:
2,3^2,19,7^2,2|a^2=g,c^a=c^2,e^a=f^5,f^a=e^3,d^b=d^11,e^b=e^4,f^b=f^4,e^c=e^2,f^c=f^4280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 610);