Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #19882 |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,56,59,58)(55,60,62,66)(57,63,65,67)(61,68,69,64)(70,73,75,81)(71,77,78,85)(72,79,74,83)(76,84,82,80);(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)(54,57,59,65)(55,61,62,69)(56,63,58,67)(60,68,66,64)(70,72,75,74)(71,76,78,82)(73,79,81,83)(77,84,85,80);(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)(54,56,59,58)(55,60,62,66)(57,63,65,67)(61,68,69,64)(70,71,75,78)(72,76,74,82)(73,80,81,84)(77,83,85,79);(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)(54,55,59,62)(56,60,58,66)(57,64,65,68)(61,67,69,63)(71,76)(72,74)(77,84)(78,82)(79,83)(80,85)Polycyclic presentation:
2^8,53|a^2=h,b^2=gh,c^2=gh,d^2=gh,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^52,d^b=de,e^b=eg,i^b=i^52,f^c=fh,i^c=i^52,e^d=eg,i^d=i^52638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 160827);