Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1654 ⋊ C2 |
| Sylow | C53 ⋊ #18561 |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
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)(55,62)(60,69)(61,66)(63,68)(70,73,76,72)(71,79,82,85)(74,84,75,83)(77,80,78,81);(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)(54,57,59,58)(55,61,62,66)(56,64,65,67)(60,68,69,63)(70,72,76,73)(71,78,82,77)(74,84,75,83)(79,81,85,80);(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)(54,56,59,65)(55,60,62,69)(57,64,58,67)(61,68,66,63)(70,72,76,73)(71,77,82,78)(74,84,75,83)(79,80,85,81);(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)(56,63,65,68)(57,61,58,66)(60,67,69,64)(70,71,76,82)(72,79,73,85)(74,81,75,80)(77,84,78,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=g,d^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,i^a=i^52,e^b=eg,f^b=fh,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 146008);