Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #7318 |
484 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 484 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 — 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)(55,60,63,74)(57,68)(58,66,71,80)(59,67)(61,64,76,79)(62,73)(65,70)(69,81,82,72)(75,78)(77,83)(84,85);(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)(54,55,58,62)(56,64,66,78)(57,61,69,75)(59,63,71,77)(60,72,73,65)(67,79,80,85)(68,74,81,83)(70,76,82,84)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,b^a=bc,c^a=cf,e^a=egh,g^a=gh,c^b=cg,d^b=dfh,f^b=fh,i^b=i^52,e^d=eh860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56870);