Finite Group DatabasebetaFinite Group Databasebeta| order | 13420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C61 ⋊ C4×C5 |
| Hall | #16809823 ⋊ C4 |
| Hall | C11⋊#6923 ⋊ C5 |
| Sylow | C61 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ #6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C61 | C4×C5 |
| prime radical | #20269516 | C2 |
| cosocle | C11×D61 | C2×C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 671 |
A minimal faithful permutation representation — 2 generators on 72 points:
(2,7,22,52,34,3,11,31,17,32,5,16,10,30,49,8,4,15,35,54)(6,26,44,61,27,13,25,51,45,47,12,29,28,60,48,24,14,46,53,38)(9,39,33,56,59,19,41,55,57,23,21,37,40,50,42,18,20,58,36,43)(63,67,68,66,71,64,65,72,69,70);(1,2,6,11,23,26,25,45,52,10,21,8,18,38,58,51,61,42,28,50,34,48,24,15,32,37,57,35,16,33,20,41,40,7,17,36,39,54,31,13,27,49,56,44,59,60,46,55,47,19,3,9,22,30,53,14,29,43,4,12,5)(62,63,66,71,65,68,72,67,70,69,64)Polycyclic presentation:
2,5,2,11,61|a^2=c,d^a=d^10,e^a=e^50,d^b=d^4,e^b=e^58,e^c=e^6055 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13420, 37);