Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1891 ⋊ C2 |
| Sylow | C53 ⋊ #21781 |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(54,58,60,72)(55,63,64,71)(56,68,69,82)(57,70,59,74)(61,76,66,80)(62,78,65,79)(67,81,73,83)(75,84,77,85);(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)(54,57,60,59)(55,62,64,65)(56,67,69,73)(58,70,72,74)(61,75,66,77)(63,78,71,79)(68,81,82,83)(76,84,80,85);(54,56)(55,61)(57,67)(58,68)(59,73)(60,69)(62,77)(63,76)(64,66)(65,75)(70,81)(71,80)(72,82)(74,83)(78,85)(79,84);(54,55,59,65,60,64,57,62)(56,66,67,75,69,61,73,77)(58,71,70,79,72,63,74,78)(68,76,83,84,82,80,81,85)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,d^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,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, 178745);