Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12292 |
310 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 63 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) = 3392 |
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)(54,57,58,64)(55,60,61,67)(56,62,63,69)(59,65,66,68)(70,72,74,75)(71,77,78,83)(73,80,82,79)(76,84,85,81);(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)(55,59)(57,62)(58,63)(60,65)(61,66)(64,69)(67,68)(70,71,74,78)(72,77,75,83)(73,81,82,84)(76,79,85,80);(54,55,58,61)(56,59,63,66)(57,60,64,67)(62,68,69,65)(71,76)(72,75)(73,80)(77,84)(78,85)(79,82)(81,83)Polycyclic presentation:
2^8,53|a^2=gh,b^2=h,c^2=g,d^2=fh,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,d^b=df,e^b=eg,f^b=fh,d^c=dg,i^c=i^52788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82851);