Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8657 |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 81 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)(59,64)(62,65)(66,68,69,75)(67,72,71,80)(70,79,77,76)(73,81,78,74);(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)(58,59,63,65,61,64,60,62)(67,71)(72,80)(73,78)(74,81);(54,55,56,57)(59,62)(60,63)(64,65)(66,67)(68,74)(69,71)(70,78)(72,76)(73,77)(75,81)(79,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=dgh,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cg,i^b=i^52,e^c=eh1034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62685);