Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #23360 |
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(55,62,63,77)(60,75,64,79)(61,68,78,82)(74,85,80,76);(54,57,58,70,59,71,73,84)(55,61,77,82,63,78,62,68)(56,65,66,69,67,81,72,83)(60,74,79,76,64,80,75,85);(54,56)(55,60)(57,69)(58,72)(59,67)(61,76)(62,79)(63,64)(65,70)(66,73)(68,80)(71,83)(74,82)(75,77)(78,85)(81,84);(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)(56,64,67,60)(57,68,71,82)(58,62)(59,63)(61,70,78,84)(65,76)(66,79,72,75)(69,74)(73,77)(80,83)(81,85)Polycyclic presentation:
2^8,53|a^2=g,c^2=ef,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,i^a=i^52,c^b=cef,d^b=de,f^b=fh,g^b=gh,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196139);