Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C9⋊((C19⋊D19)⋊C5) |
| unambiguous semidirect product | (C9⋊(C19⋊D19))⋊C5 |
| Fitting, derived, Hall | C9×C192 ⋊ C2×C5 |
| Hall | C9×C192⋊C5 ⋊ C2 |
| Hall | C9⋊(C19⋊D19) ⋊ C5 |
| Hall | C192⋊C5 ⋊ D9 |
| Sylow | C192 ⋊ C5×D9 |
| Sylow | C9 ⋊ (C19⋊D19)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C192 | C2×C5 |
| Frattini | C3 | C3⋊((C19⋊D19)⋊C5) |
| socle | C3×C192 | C5×D3 |
| LCS | G ▷ C9×C192 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 104 |
| transitive degree | μt(G) = 855 |
A minimal faithful permutation representation — 2 generators on 104 points:
(2,4)(3,7)(5,6)(8,9)(10,11,13,19,34)(12,28,21,36,73,16,17,41,42,62)(14,44,46,89,97,22,23,61,76,104)(15,37,38,58,81,26,20,64,66,84)(18,54,43,63,87,31,32,74,75,92)(24,47,79,98,33,25,49,77,99,55)(27,68,59,60,103,50,39,35,85,86)(29,71,78,82,83,53,48,90,57,101)(30,69,70,91,100,45,40,93,95,102)(51,72,94,88,80,52,65,67,96,56);(1,9,4,7,6,5,3,2,8)(10,12,18,33,56,81,100,101,104,86,103,97,83,102,84,80,55,31,16)(11,14,24,26,30,54,50,17,29,52,51,53,28,27,32,45,15,25,22)(13,20,39,65,21,40,23,47,43,71,48,74,49,44,69,41,72,68,37)(19,35,36,61,63,90,77,70,94,38,64,67,93,79,78,75,46,42,59)(34,57,66,92,85,99,96,89,73,91,95,62,76,88,98,60,87,58,82)Polycyclic presentation:
2,5,3,19^2,3|c^3=f^2,c^a=c^2f,d^a=d^18,e^a=e^18,f^a=f^2,d^b=d^12e^8,e^b=d^14e^11354 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 44);