Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2250 ⋊ C2 |
| Sylow | C53 ⋊ #33834 |
702 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)(58,62)(59,63)(60,70)(61,72)(64,78)(65,76)(67,73)(68,77)(69,83)(71,82)(74,87)(75,85)(81,86)(84,89);(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)(58,61,65,75)(59,67,64,74)(60,69,70,83)(62,72,76,85)(63,73,78,87)(66,80,79,88)(68,81,82,89)(71,84,77,86);(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)(58,60,65,70)(59,66,64,79)(61,69,75,83)(62,77,76,71)(63,68,78,82)(67,80,74,88)(72,86,85,84)(73,81,87,89);(54,55)(56,57)(58,59)(60,68)(61,67)(62,76)(64,65)(66,71)(69,81)(70,82)(72,85)(74,75)(77,79)(80,84)(83,89)(86,88)Polycyclic presentation:
2^8,53|b^2=h,c^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^b=i^52,i^c=i^52,e^d=eg,g^d=gh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326085);