Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13015 |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 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)(62,64,68,79)(63,70,74,89)(65,81,66,84)(67,85,82,78)(69,86,87,75)(71,90,72,92)(73,93,91,88)(76,83,77,80);(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)(54,56,57,55)(59,61)(63,69)(65,80)(66,83)(67,82)(70,86)(71,73)(72,91)(74,87)(75,89)(76,81)(77,84)(78,85)(88,92)(90,93);(54,55,57,56)(58,59,60,61)(62,63,66,72,82,91,80,69,68,74,65,71,67,73,83,87)(64,75,77,93,85,90,81,89,79,86,76,88,78,92,84,70)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,c^2=h,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,f^c=fg,g^c=gh,i^c=i^522138 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86645);