Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C53×#3027 ⋊ C2 |
| Sylow | C53 ⋊ #32894 |
3638 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 3638 conjugacy classes of subgroups — too many to draw. Only its 247 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:
(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)(55,63)(56,68)(58,74)(59,71)(60,72)(61,76)(62,64)(65,78)(66,79)(67,82)(69,84)(70,85)(73,83)(75,80)(77,81);(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)(54,57)(55,62)(56,68)(58,71)(59,74)(60,72)(61,75)(63,64)(65,79)(66,78)(67,81)(69,83)(70,85)(73,84)(76,80)(77,82);(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)(55,61)(57,68)(58,73)(59,69)(60,70)(62,75)(63,76)(64,80)(65,67)(66,77)(71,84)(72,85)(74,83)(78,82)(79,81);(54,55)(56,67)(57,63)(58,65)(59,64)(60,66)(61,69)(62,71)(68,75)(70,80)(72,79)(73,77)(74,78)(76,83)(81,84)(82,85)Polycyclic presentation:
2^8,53|e^2=h,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,f^a=fh,e^b=eh,g^b=gh,i^b=i^52,f^c=fh,i^c=i^52,e^d=eh800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 318311);