Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2211 ⋊ C2 |
| Sylow | C53 ⋊ #33832 |
686 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)(59,65)(60,70)(61,75)(62,76)(64,80)(67,68)(69,82)(71,72)(73,88)(74,83)(77,84)(78,79)(81,85)(87,89);(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)(55,57);(58,60,63,73)(59,64,68,82)(61,70,77,88)(62,78,76,72)(65,81,67,87)(66,85,86,89)(69,83,80,74)(71,84,79,75);(54,55)(56,57)(58,59,63,68)(60,69,73,80)(61,74,77,83)(62,65,76,67)(64,79,82,71)(66,84,86,75)(70,87,88,81)(72,89,78,85)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,g^a=gh,d^b=de,e^b=eg,g^b=gh,i^c=i^52,e^d=eg,g^d=gh,i^d=i^52797 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326051);