Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11309 |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(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)(54,57)(55,61,62,76)(56,65)(58,71)(59,69)(60,73,64,80)(63,79,78,77)(66,83)(67,82)(68,84)(70,72)(74,85,81,75);(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)(55,60)(57,68,69,83)(58,66)(59,67)(61,75,76,85)(62,64)(63,74)(65,70,82,71)(72,84)(73,77,80,79)(78,81);(54,55)(56,64,67,60)(57,61,69,76)(58,63)(59,62)(65,80)(66,81,84,74)(68,85)(70,77,71,79)(72,78)(73,82)(75,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=de,c^2=d,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cf,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78087);