Finite Group DatabasebetaFinite Group Databasebeta| order | 22914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439405 |
| Fitting, socle, derived | C3×C19×C67 ⋊ C2×C3 |
| Hall | C3×#16838390 ⋊ C2 |
| Hall | C19×C67 ⋊ C3×D3 |
| Sylow | C67 ⋊ D3×C19⋊C3 |
| Sylow | C19 ⋊ C3⋊(D67⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C67 | C2×C3 |
| LCS | G ▷ C3×C19×C67 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3819 |
A minimal faithful permutation representation — 2 generators on 89 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,70,72)(71,74,75)(73,77,76)(78,82,80)(79,83,81)(84,86,85)(88,89);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,69,71,75,80,85,82,70,73,78,83,72,76,81,74,79,84,86,77)(87,88,89)Polycyclic presentation:
2,3^2,19,67|c^a=c^2,e^a=e^66,d^b=d^7,e^b=e^37654 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22914, 64);