Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1886 ⋊ C2 |
| Sylow | C53 ⋊ #21476 |
1322 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)(54,56,57,55)(61,72)(65,80)(69,86)(73,76)(78,89)(81,83)(84,85)(87,88);(58,61,63,72)(59,65,67,80)(60,69,71,86)(62,76,77,73)(64,78,79,89)(66,83,74,81)(68,84,82,85)(70,88,75,87);(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)(59,64)(61,69)(62,75)(63,71)(65,78)(66,82)(67,79)(68,74)(70,77)(72,86)(73,88)(76,87)(80,89)(81,84)(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)(54,55,57,56)(58,59,63,67)(60,68,71,82)(61,65,72,80)(62,74,77,66)(64,75,79,70)(69,85,86,84)(73,83,76,81)(78,88,89,87)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,d^2=gh,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 175524);