Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13634 |
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(59,66)(64,74)(67,81)(68,82)(75,87)(76,88)(77,84)(83,89);(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)(58,59,65,76,61,67,78,84,72,82,86,89,85,87,71,74,63,66,80,88,73,81,70,77,62,68,79,83,69,75,60,64);(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)(54,55,56,57)(59,64)(60,65)(61,69)(62,72)(66,74)(67,83)(68,84)(70,86)(71,80)(73,85)(75,76)(77,82)(78,79)(81,89)(87,88)Polycyclic presentation:
2^8,53|a^2=e,b^2=df,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^52,c^b=ch,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90076);