Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #29231 |
404 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)(54,57,58,73,60,72,59,74)(55,63,64,71,65,79,61,76)(56,68,67,81,70,84,69,83)(62,78,66,80,77,82,75,85);(54,56)(55,62,65,77)(57,68)(58,67)(59,69)(60,70)(61,75,64,66)(63,78,79,82)(71,80,76,85)(72,84)(73,81)(74,83);(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)(55,61,65,64)(56,67,70,69)(57,72)(62,77)(63,71,79,76)(66,75)(68,83,84,81)(73,74);(54,55,60,65)(56,66)(57,71,72,76)(58,61,59,64)(62,67)(63,74,79,73)(68,82)(69,77)(70,75)(78,84)(80,81)(83,85)Polycyclic presentation:
2^8,53|a^2=fg,b^2=eg,c^2=ef,d^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,d^b=dh,i^b=i^52,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 270363);