Finite Group DatabasebetaFinite Group Databasebeta| order | 22914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439409 |
| Fitting, socle, derived | C3×C19×C67 ⋊ C2×C3 |
| Hall | C3×#16838390 ⋊ C2 |
| Hall | C19×C67 ⋊ C3×D3 |
| Sylow | C67 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ D3×C67⋊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:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,43)(28,39,47)(31,42,44)(34,45,41)(36,48,38)(40,52,54)(46,56,55)(49,58,53)(50,57,51)(59,63,62)(60,64,61)(65,67,66)(69,73,74,70,71,75)(72,81,78,76,77,83)(79,84,86,85,82,80)(88,89);(1,2,4,8,15,25,27,7,13,21,31,43,54,52,24,36,49,59,64,48,22,32,44,55,62,66,63,45,20,5,9,16,26,38,51,42,17,3,6,11,18,28,40,39,14,23,34,46,57,35,47,37,50,60,65,67,58,33,12,19,29,41,53,61,56,30,10)(68,69,72,78,84,81,85,71,75,80,86,74,73,79,77,82,83,76,70)(87,88,89)Polycyclic presentation:
2,3^2,19,67|c^a=c^2,d^a=d^18,d^b=d^7,e^b=e^37678 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22914, 60);