Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11456 |
364 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 127 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:
(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)(56,66)(61,76)(65,81)(67,69)(68,72)(75,83)(77,85)(82,84);(54,56)(55,61,64,76)(57,67)(58,72)(59,69)(60,66)(62,65,70,81)(63,77,80,85)(68,74)(71,83)(73,75)(78,82,79,84);(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)(54,55,58,63,59,62,73,78,60,64,74,80,57,70,71,79)(56,65,68,82,69,76,83,85,66,81,72,84,67,61,75,77)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,d^2=h,e^2=g,g^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=ch,e^b=efh,e^d=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78756);