Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13720 |
182 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 93 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)(55,59)(58,61)(62,65,66,74,86,79,93,82,69,73,83,75,90,88,67,84,70,85,71,80,76,92,89,64,77,78,91,63,68,72,87,81);(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)(54,56,57,60)(55,58,59,61)(62,64,67,79,68,80,83,65,77,84,93,72,76,75,66,78,70,82,87,92,90,74,91,85,69,81,89,88,86,63,71,73);(54,55)(56,58)(57,59)(60,61)(62,63,70,75)(64,76,82,86)(65,83,85,91)(66,78,71,73)(67,88,87,72)(68,81,90,84)(69,80,77,74)(79,93,92,89)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,g^a=gh,i^c=i^521058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90539);