Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12365 |
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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)(54,57)(55,62)(56,66)(58,70)(59,74)(60,76)(61,77)(63,79)(64,81)(65,82)(67,84)(68,80)(69,72)(71,83)(73,85)(75,78);(54,56,58,67)(55,61,63,65)(57,66,70,84)(59,60,71,72)(62,77,79,82)(64,80,75,73)(68,78,85,81)(69,74,76,83);(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)(54,55)(56,65)(57,68,70,85)(58,63)(59,73)(60,75)(61,67)(62,66,79,84)(64,72)(69,77,76,82)(71,80)(74,81,83,78)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^52,d^b=df,e^b=eg,g^b=gh,d^c=dg,e^c=egh,f^c=fh,g^c=gh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83332);