Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1395 ⋊ C2 |
| Sylow | C53 ⋊ #12634 |
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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 — 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)(54,57,59,63,60,70,74,55)(56,65,67,76,68,81,82,61)(58,69,72,71,73,83,77,62)(64,66,78,75,79,80,85,84);(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)(55,61)(57,65)(58,66,73,80)(59,67)(60,68)(62,64,71,79)(63,76)(69,78,83,85)(70,81)(72,75,77,84)(74,82);(54,55,59,57,60,63,74,70)(56,64,67,78,68,79,82,85)(58,71,72,83,73,62,77,69)(61,75,65,80,76,84,81,66)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,e^2=h,b^a=bd,c^a=ch,d^a=dh,f^a=fgh,d^b=dg,g^b=gh,i^c=i^52,f^d=fh722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84766);