Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1951 ⋊ C2 |
| Sylow | C53 ⋊ #26080 |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(62,66,67,81,68,82,69,83)(63,72,73,80,74,88,84,93)(64,75,76,90,65,78,79,92)(70,85,71,87,86,89,77,91);(54,56,57,61)(55,58,59,60)(62,65,68,64)(63,71,74,77)(66,78,82,75)(67,79,69,76)(70,73,86,84)(72,87,88,91)(80,89,93,85)(81,92,83,90);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(62,64,67,76,68,65,69,79)(63,70,73,71,74,86,84,77)(66,75,81,90,82,78,83,92)(72,85,80,87,88,89,93,91);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,57,59)(56,60,61,58)(62,63,68,74)(64,71,65,77)(66,80,82,93)(67,84,69,73)(70,79,86,76)(72,83,88,81)(75,89,78,85)(87,92,91,90)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,c^2=f,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,g^c=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 228457);