Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #33126 |
742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(62,65,66,78,67,79,73,87)(63,70,71,84,69,77,80,92)(64,75,76,90,74,88,81,93)(68,82,72,85,83,91,86,89);(55,59)(58,61)(63,69)(64,74)(70,77)(71,80)(75,88)(76,81)(84,92)(90,93);(54,56,57,60)(55,58,59,61)(62,64,73,81,67,74,66,76)(63,68,80,86,69,83,71,72)(65,75,87,93,79,88,78,90)(70,82,92,89,77,91,84,85);(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)(56,58)(57,59)(60,61)(62,63,67,69)(64,72,74,86)(65,77,79,70)(66,80,73,71)(68,81,83,76)(75,89,88,85)(78,84,87,92)(82,90,91,93)Polycyclic presentation:
2^8,53|a^2=h,b^2=ef,d^2=e,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^52,c^b=ch,g^d=gh,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 320572);