Finite Group DatabasebetaFinite Group Databasebeta| order | 20102 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C19⋊(C23⋊D23) |
| unambiguous semidirect product | C23⋊D437 |
| Fitting, socle, derived, Hall | C19×C232 ⋊ C2 |
| Sylow | C232 ⋊ D19 |
| Sylow | C19 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C232 | C2 |
| LCS | G ▷ C19×C232 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 10051 |
A minimal faithful permutation representation — 3 generators on 65 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(43,44,46,48,50,52,54,56,58,60,62,64,65,63,61,59,57,55,53,51,49,47,45);(20,21,23,25,27,29,31,33,35,37,39,41,42,40,38,36,34,32,30,28,26,24,22)Polycyclic presentation:
2,19,23^2|b^a=b^18,c^a=c^22,d^a=d^225027 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20102, 10);