Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#2296 ⋊ C2 |
| Sylow | C53 ⋊ #34866 |
1782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 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)(54,56,57,60)(55,59,58,61)(62,65,66,64)(63,67,68,69);(62,64,66,65)(63,69,68,67)(71,75)(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)(63,68)(67,69)(70,72,73,77)(71,74,75,76);(55,58)(59,61)(62,64,66,65)(63,67,68,69)(70,71)(72,76)(73,75)(74,77);(54,55)(56,59)(57,58)(60,61)(62,63)(64,69)(65,67)(66,68)Polycyclic presentation:
2^8,53|b^2=g,c^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^c=i^521532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 340341);