Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1791 ⋊ C2 |
| Sylow | C53 ⋊ #21484 |
1306 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 251 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)(54,58,59,63,60,71,72,55)(56,65,67,74,66,80,81,61)(57,68,70,75,69,82,83,62)(64,77,79,76,78,85,84,73);(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)(56,64)(58,68)(59,70)(60,69)(61,73)(63,75)(65,77)(66,78)(67,79)(71,82)(72,83)(74,76)(80,85)(81,84);(54,56)(55,61)(57,64)(58,65)(59,67)(60,66)(62,73)(63,74)(68,77)(69,78)(70,79)(71,80)(72,81)(75,76)(82,85)(83,84);(54,55,59,58,60,63,72,71)(56,61,67,65,66,74,81,80)(57,62,70,68,69,75,83,82)(64,76,79,85,78,73,84,77)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,f^b=fh,e^c=eh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 175582);