Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2163 ⋊ C2 |
| Sylow | C53 ⋊ #33676 |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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)(54,56,57,60)(55,59,58,61)(62,65,68,67)(63,71,73,81)(64,74,77,76)(66,78,80,79)(69,83,85,91)(70,86,87,72)(75,88,90,89)(82,92,93,84);(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)(63,70)(65,67)(66,79)(69,82)(71,72)(73,87)(74,76)(75,89)(78,80)(81,86)(83,84)(85,93)(88,90)(91,92);(55,58)(59,61)(62,64,68,77)(63,69,73,85)(65,74,67,76)(66,75,80,90)(70,82,87,93)(71,83,81,91)(72,84,86,92)(78,88,79,89);(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)(56,59)(57,58)(60,61)(62,63,68,73)(64,69,77,85)(65,71,67,81)(66,70,80,87)(72,78,86,79)(74,83,76,91)(75,82,90,93)(84,88,92,89)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=eh,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,d^c=dh,f^c=fg,g^c=gh,i^c=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324655);