Finite Group DatabasebetaFinite Group Databasebeta| order | 20140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11761505 |
| Fitting, socle, derived, Hall | C5×C19×C53 ⋊ C4 |
| Hall | C19×C53 ⋊ AGL(1,𝔽5) |
| Hall | C5×C53 ⋊ Dic19 |
| Hall | C5×C19 ⋊ #6157 |
| Sylow | C53 ⋊ C19⋊AGL(1,𝔽5) |
| Sylow | C19 ⋊ #11761505 |
| Sylow | C5 ⋊ C19⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C53 | C4 |
| prime radical, cosocle | C19×D265 | C2 |
| LCS | G ▷ C5×C19×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 5035 |
A minimal faithful permutation representation — 2 generators on 77 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,43)(23,34,35,40)(27,32,38,37)(29,41,42,33)(36,44,45,50)(39,46,47,49)(48,51,52,53)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(74,75,76,77);(1,2,5,10,19,32,21,8,16,27,39,48,51,44,30,42,28,40,49,45,35,22,13,6,11,20,33,41,25,12,3,7,14,23,36,46,34,17,29,43,50,53,52,47,38,26,15,24,37,31,18,9,4)(54,55,57,59,61,63,65,67,69,71,72,70,68,66,64,62,60,58,56)(73,74,75,77,76)Polycyclic presentation:
2^2,5,19,53|a^2=b,c^a=c^2,d^a=d^18,e^a=e^30,c^b=c^4,e^b=e^521276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20140, 18);