Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1900 ⋊ C2 |
| Sylow | C53 ⋊ #33125 |
794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 points:
(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)(62,64,65,71,66,70,72,77)(63,69,67,74,68,75,73,76);(55,59)(58,61)(63,68)(67,73)(69,75)(74,76);(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)(54,56,57,60)(55,58,59,61)(62,63,65,67,66,68,72,73)(64,69,71,74,70,75,77,76);(54,55)(56,58)(57,59)(60,61)(63,67)(64,70)(65,72)(68,73)(69,76)(74,75)Polycyclic presentation:
2^8,53|b^2=ef,d^2=e,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,c^b=ch,i^b=i^52,g^d=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 320560);