Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1951 ⋊ C2 |
| Sylow | C53 ⋊ #22691 |
846 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)(58,62)(59,68)(60,74)(61,75)(63,82)(64,80)(65,73)(66,77)(67,84)(69,89)(70,87)(71,88)(72,86)(76,78)(79,81)(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)(58,61,63,74,65,79,64,78)(59,67,69,85,71,86,70,77)(60,73,81,80,76,62,75,82)(66,68,84,89,83,88,72,87);(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)(58,60)(59,66)(61,73)(62,79)(63,81)(64,75)(65,76)(67,68)(69,84)(70,72)(71,83)(74,80)(77,87)(78,82)(85,89)(86,88);(54,55,56,57)(58,59)(60,72)(61,77)(62,68)(63,70)(64,69)(65,71)(66,75)(67,78)(73,88)(74,86)(76,84)(79,85)(80,89)(81,83)(82,87)Polycyclic presentation:
2^8,53|a^2=g,c^2=fh,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=de,e^b=eh,i^b=i^52,i^c=i^52,e^d=eh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 188058);