Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #22745 |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 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)(58,61,62,60)(59,64,63,65)(66,69,70,77)(67,72,74,73)(68,78,76,81)(71,80,79,75);(58,60,62,61)(59,64,63,65)(66,68,77,81,70,76,69,78)(67,71,72,80,74,79,73,75);(58,59,62,63)(60,64,61,65)(68,76)(71,79)(75,80)(78,81);(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)(54,55,56,57)(59,63)(64,65)(66,67)(68,75)(69,72)(70,74)(71,78)(73,77)(76,80)(79,81)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,c^2=efh,d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^52,c^b=ch,d^b=de1514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 188566);