Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7351 |
178 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 39 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 — 2 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)(54,56)(55,60,61,73)(57,67)(58,70)(59,64)(62,72,75,80)(63,78,76,74)(65,68)(66,71)(69,79)(77,85,84,83)(81,82);(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)(54,55,57,62,58,63,69,77,59,61,68,75,71,76,82,84)(56,60,65,72,66,74,79,83,64,73,67,80,70,78,81,85)Polycyclic presentation:
2^8,53|a^2=d,b^2=g,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,c^b=ch,d^b=de,f^b=fh,i^b=i^52,d^c=dg,e^d=eh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56944);