Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1630 ⋊ C2 |
| Sylow | C53 ⋊ #18751 |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 85 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)(71,76)(75,84)(77,81)(78,85);(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)(54,57,59,58)(55,61,62,66)(56,64,65,67)(60,68,69,63)(70,72)(71,75)(73,83)(74,79)(76,84)(77,85)(78,81)(80,82);(54,56)(55,60)(57,64)(58,67)(59,65)(61,68)(62,69)(63,66)(73,82)(77,81)(78,85)(80,83);(54,55,59,62)(56,63,65,68)(57,61,58,66)(60,67,69,64)(70,71)(72,78)(73,81)(74,76)(75,80)(77,82)(79,85)(83,84)Polycyclic presentation:
2^8,53|a^2=g,c^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fh,e^b=eg,f^b=fh,e^c=eh,f^c=fh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 148078);