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 | #22582225 ⋊ 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 | #31822467 | 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)(20,41,46,42,28,30,29,52,43,27,44,47)(23,45,68,34,36,61,37,53,54,35,55,40)(33,56,74,67,50,69,51,70,64,49,62,60)(38,72,66,63,58,65,59,71,48,57,73,75);(1,2,5,6,4,7,3)(8,9,11,13,10,12,14)(15,16,20,30,48,58,72,70,55,59,37,22,34,18,26,40,62,65,54,41,51,32,42,63,67,74,28,45,46,39,60,69,31,43,53,44,64,49,57,27,21,33,52,68,75,50,61,24,25,35,17,23,38,36,56,71,73,66,47,29,19)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^13,f^c=f^60279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 220);