Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#2492 ⋊ C2 |
| Sylow | C53 ⋊ #26722 |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
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)(55,58)(59,61)(62,64,65,68)(63,67,66,69);(54,56,57,60)(55,59,58,61)(63,66)(67,69)(70,71,73,75)(72,77,76,74);(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)(55,58)(59,61)(71,74)(72,76)(75,77);(54,55)(56,59)(57,58)(60,61)(62,63)(64,67)(65,66)(68,69)Polycyclic presentation:
2^8,53|c^2=eh,d^2=f,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,i^b=i^52,g^c=gh1040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 237625);