Finite Group DatabasebetaFinite Group Databasebeta| order | 22990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊((C11⋊C5)⋊D11) |
| unambiguous semidirect product | (C11⋊C5)⋊D209 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C2×C5 |
| Hall | C11×C19×C11⋊C5 ⋊ C2 |
| Hall | C11⋊D209 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ D19 |
| Sylow | C112 ⋊ C5×D19 |
| Sylow | C19 ⋊ (C11⋊C5)⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C2×C5 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1045 |
A minimal faithful permutation representation — 2 generators on 41 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,25,26,24,29,22,23,30,27,28)(32,33)(34,35)(36,37)(38,39)(40,41);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,24,29,23,26,30,25,28,27,22)(31,32,34,36,38,40,41,39,37,35,33)Polycyclic presentation:
2,5,11^2,19|c^a=c^10,d^a=d^10,e^a=e^18,c^b=c^4739 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22990, 20);