Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1979 ⋊ C2 |
| Sylow | C53 ⋊ #25145 |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(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)(55,57)(58,62,63,64)(59,67,68,77)(60,70,71,78)(61,74,76,75)(65,80,81,89)(66,83,84,72)(69,86,73,87)(79,88,82,85);(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)(58,61)(59,66)(60,69)(62,74)(63,76)(64,75)(65,79)(67,83)(68,84)(70,86)(71,73)(72,77)(78,87)(80,88)(81,82)(85,89);(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)(55,57)(58,60,62,70,63,71,64,78)(59,65,67,80,68,81,77,89)(61,73,75,86,76,69,74,87)(66,82,72,88,84,79,83,85);(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)(56,57)(58,59,64,77,63,68,62,67)(60,65,78,89,71,81,70,80)(61,72,74,66,76,83,75,84)(69,85,86,79,73,88,87,82)Polycyclic presentation:
2^8,53|a^2=fh,b^2=f,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,f^c=fh,i^c=i^52,i^d=i^52875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 216903);