Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #29386 |
654 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 4 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)(55,63,65,64)(61,76,77,66)(62,79,80,70)(75,85,78,81);(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)(54,57)(55,62)(56,67)(58,71)(59,74)(60,72)(61,75)(63,79)(64,70)(65,80)(66,81)(68,82)(69,84)(73,83)(76,85)(77,78);(54,56,58,68,60,69,59,73)(55,61,64,66,65,77,63,76)(57,67,71,82,72,84,74,83)(62,78,70,85,80,75,79,81);(54,55)(56,66)(57,70)(58,63)(59,64)(60,65)(61,68)(62,71)(67,75)(69,76)(72,79)(73,77)(74,80)(78,84)(81,83)(82,85)Polycyclic presentation:
2^8,53|b^2=e,d^2=g,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,f^b=fh,f^c=fh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 272038);