Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C72×C19 ⋊ C2×C3×D3 |
| derived | C19×#3862 ⋊ C22×C3 |
| Hall | #22552728 ⋊ C22 |
| Sylow | C72 ⋊ C2×C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ (#64418⋊C2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#3862 | C22×C3 |
| Fitting, socle | C72×C19 | C2×C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
152 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 152 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) = 33 |
| transitive degree | μt(G) = 266 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,3,9,7,13,8)(2,4)(5,12)(6,10)(15,16,22)(17,26,30)(18,20,27)(19,29,21)(23,32,28)(24,31,33);(1,2)(3,6)(4,9)(5,7)(8,11)(10,14)(12,13)(16,17)(18,20)(19,23)(21,22)(24,28)(25,30)(26,32)(27,33)(29,31)Polycyclic presentation:
2^2,3^2,19,7^2|d^a=d^2,e^a=e^18,f^a=f^4g,g^a=f^6g^3,f^b=f^6,g^b=g^6,e^c=e^7,f^c=f^2,g^c=g^2,f^d=f^2g^6,g^d=g^467 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 801);