Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1868 ⋊ C2 |
| Sylow | C53 ⋊ #29902 |
772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,57)(55,63)(56,67)(58,70)(59,71)(60,72)(61,74)(62,77)(64,79)(65,78)(66,80)(68,82)(69,81)(73,83)(75,84)(76,85);(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)(55,62)(56,66)(57,70)(59,60)(61,73)(63,78)(64,65)(67,80)(68,69)(74,83)(77,79)(81,82);(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)(54,56,59,66,58,69,60,68)(55,61,65,75,64,73,62,76)(57,67,71,80,70,81,72,82)(63,74,78,84,79,83,77,85);(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)(56,61)(57,63)(58,64)(59,62)(60,65)(66,76)(67,74)(68,75)(69,73)(70,79)(71,77)(72,78)(80,85)(81,83)(82,84)Polycyclic presentation:
2^8,53|b^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^52,c^b=cg,e^b=eh,i^b=i^52,d^c=de,f^c=fh,g^c=gh,i^c=i^52,g^d=gh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 277872);