Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2211 ⋊ C2 |
| Sylow | C53 ⋊ #33867 |
546 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)(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)(56,61)(58,60);(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)(62,65,68,77)(63,70,72,86)(64,73,67,83)(66,79,81,93)(69,84,82,85)(71,87,88,89)(74,90,80,76)(75,91,92,78);(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)(55,58)(57,61)(59,60)(62,64,68,67)(63,69,72,82)(65,73,77,83)(66,74,81,80)(70,84,86,85)(71,78,88,91)(75,89,92,87)(76,79,90,93);(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)(64,69)(65,75)(66,78)(67,82)(68,72)(70,76)(71,80)(73,89)(74,88)(77,92)(79,84)(81,91)(83,87)(85,93)(86,90)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,d^b=de,i^b=i^52,f^c=fg,g^c=gh,i^c=i^52,i^d=i^52809 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326472);