Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2884 ⋊ C2 |
| Sylow | C53 ⋊ #33349 |
1190 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 271 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)(54,57,59,69)(55,62,63,77)(56,64,66,67)(58,68,71,83)(60,73,70,82)(61,74,75,76)(65,78,80,81)(72,84,79,85);(54,56,59,66)(55,61,63,75)(57,67,69,64)(58,65,71,80)(60,72,70,79)(62,76,77,74)(68,81,83,78)(73,85,82,84);(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)(55,60)(61,72)(62,73)(63,70)(74,84)(75,79)(76,85)(77,82);(54,55)(56,61)(57,62)(58,70,71,60)(59,63)(64,74)(65,79,80,72)(66,75)(67,76)(68,82,83,73)(69,77)(78,85,81,84)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,b^a=be,e^a=eg,g^a=gh,f^b=fg,i^b=i^52,d^c=dh,f^e=fh1112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322322);