Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C61 ⋊ C3×C4 |
| Hall | C7×C7⋊#6923 ⋊ C3 |
| Hall | #22582226 ⋊ C4 |
| Sylow | C61 ⋊ #10596873 |
| Sylow | C72 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C61 | C3×C4 |
| prime radical | #31822466 | C2 |
| cosocle | C72×D61 | C2×C3 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 854 |
A minimal faithful permutation representation — 2 generators on 75 points:
(2,6,5,3,4,7)(9,10,11)(12,14,13)(16,21,26,22,18,31,19,32,24,17,25,39)(20,30,56,40,28,44,29,45,41,27,42,58)(23,49,67,33,35,57,36,38,50,34,51,43)(37,60,74,55,46,73,53,69,61,52,62,75)(47,66,54,71,64,68,59,48,70,63,72,65);(1,2,5,6,4,7,3)(8,9,11,13,10,12,14)(15,16,20,30,46,61,73,65,67,53,36,22,33,24,25,38,54,60,35,44,59,39,40,55,71,72,41,57,42,32,48,66,21,28,43,56,64,63,52,27,31,47,58,51,69,70,49,18,26,34,17,23,37,50,68,75,74,62,45,29,19)Polycyclic presentation:
2,3,2,7^2,61|a^2=c,d^a=d^6,f^a=f^50,d^b=d^4,e^b=e^4,f^b=f^47,f^c=f^60279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 219);