Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1532 ⋊ C2 |
| Sylow | C53 ⋊ #8498 |
692 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(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)(56,61)(58,60)(62,65,68,81)(63,70,71,85)(64,75,77,91)(66,80,67,79)(69,83,74,88)(72,86,73,78)(76,92,82,90)(84,89,87,93);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,55)(56,60)(57,59)(58,61)(62,64)(63,69)(65,75)(66,76)(67,82)(68,77)(70,83)(71,74)(72,84)(73,87)(78,93)(79,90)(80,92)(81,91)(85,88)(86,89);(55,58,59,60)(62,63,67,73,68,71,66,72)(64,74,76,87,77,69,82,84)(65,78,80,70,81,86,79,85)(75,89,90,83,91,93,92,88)Polycyclic presentation:
2^8,53|a^2=f,c^2=g,d^2=h,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,e^c=eg,f^c=fg,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61959);