Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2047 ⋊ C2 |
| Sylow | C53 ⋊ #25317 |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(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)(54,56,57,61)(55,59,58,60)(63,70)(68,72)(69,86)(71,87)(76,88)(83,85)(84,89)(90,93);(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)(62,65,66,78)(63,69,70,86)(64,73,74,77)(67,81,80,79)(68,83,72,85)(71,88,87,76)(75,92,82,91)(84,90,89,93);(55,58)(59,60)(62,64,67,75,66,74,80,82)(63,68,71,84,70,72,87,89)(65,77,79,92,78,73,81,91)(69,85,76,90,86,83,88,93);(54,55)(56,60)(57,58)(59,61)(62,63,67,71,66,70,80,87)(64,72,75,89,74,68,82,84)(65,76,79,86,78,88,81,69)(73,90,91,83,77,93,92,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=h,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,f^c=fh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 219389);