Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #22898 |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,58)(55,63)(56,60)(57,72)(59,69)(61,65)(62,79)(64,78)(66,67)(68,75)(70,76)(71,77)(73,84)(74,85)(80,83)(81,82);(54,57)(55,62)(56,68)(58,72)(59,73)(60,75)(61,77)(63,79)(64,80)(65,71)(66,81)(67,82)(69,84)(70,85)(74,76)(78,83);(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)(54,56,59,70,60,58,76,69)(55,61,65,67,66,78,64,63)(57,68,73,85,75,72,74,84)(62,77,71,82,81,83,80,79);(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)(54,55,59,65,60,66,76,64)(56,67,70,78,58,63,69,61)(57,71,73,81,75,80,74,62)(68,83,85,79,72,77,84,82)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=de,e^b=eh,i^b=i^52,f^c=fh,e^d=eh884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 190438);