Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C61 ⋊ C3×C4 |
| Hall | C7⋊Dic427 ⋊ C3 |
| Hall | #22582225 ⋊ C4 |
| Sylow | C61 ⋊ #10596874 |
| Sylow | C72 ⋊ Dic61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31822440 |
| commutator, hypocenter | C72×C61 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C61 | C2×C3 |
| prime radical | C2×#22582225 | C2 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 11956 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2,3,4)(6,9,10,7,8,11)(13,16,17,14,15,18)(20,24,25,21,22,26)(23,32,33,27,28,42)(29,45,46,35,36,58)(30,44,40,38,34,31)(37,63,64,48,49,74)(39,61,62,50,47,55)(41,43,60,52,53,56)(51,76,77,66,65,72)(54,59,75,68,67,73)(57,79,78,70,71,69);(12,13,15,18,17,16,14)(19,20,23,29,37,49,65,71,73,74,68,52,40,25,24,30,39,51,67,36,47,56,58,72,78,62,33,44,32,43,57,70,53,28,34,42,55,69,77,46,60,61,45,59,66,50,38,22,26,31,41,54,64,75,79,76,63,48,35,27,21);(5,6,8,11,10,9,7)Polycyclic presentation:
2,3,7^2,61,2|a^2=f,c^a=c^6,d^a=d^6,e^a=e^60,c^b=c^2,d^b=d^2,e^b=e^471008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 92);