Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1979 ⋊ C2 |
| Sylow | C53 ⋊ #28505 |
998 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)(58,61,74,82,63,76,62,75)(59,66,64,78,68,83,67,73)(60,70,69,84,72,87,71,86)(65,79,77,88,81,89,80,85);(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)(55,57)(58,60)(59,65)(61,70)(62,71)(63,72)(64,77)(66,79)(67,80)(68,81)(69,74)(73,85)(75,86)(76,87)(78,88)(82,84)(83,89);(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)(59,64,68,67)(60,69,72,71)(66,78,83,73)(70,84,87,86);(54,55,56,57)(58,59,63,68)(60,65,72,81)(61,73,76,78)(62,64,74,67)(66,82,83,75)(69,80,71,77)(70,85,87,88)(79,84,89,86)Polycyclic presentation:
2^8,53|a^2=fh,b^2=egh,d^2=eh,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,i^b=i^52,g^c=gh,i^c=i^52,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 261503);