Finite Group DatabasebetaFinite Group Databasebeta| order | 20060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C59⋊#66772 |
| Fitting, socle, derived, Hall | C5×C17×C59 ⋊ C4 |
| Hall | C17×C59 ⋊ Dic5 |
| Hall | C5×C59 ⋊ #595 |
| Hall | C5×C17 ⋊ Dic59 |
| Sylow | C59 ⋊ #66772 |
| Sylow | C17 ⋊ Dic295 |
| Sylow | C5 ⋊ C59⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C59 | C4 |
| prime radical, cosocle | C5×D17×C59 | C2 |
| LCS | G ▷ C5×C17×C59 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 5015 |
A minimal faithful permutation representation — 2 generators on 81 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(61,62,63,65)(64,67,68,72)(66,71,69,70)(73,75,76,74)(78,79)(80,81);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(60,61,64,69,65,70,74,76,72,67,73,75,71,62,66,68,63)(77,78,80,81,79)Polycyclic presentation:
2^2,5,17,59|a^2=b,c^a=c^4,d^a=d^13,e^a=e^58,d^b=d^161478 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20060, 23);