Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12946 |
402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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)(58,60)(59,66)(61,72)(62,77)(63,73)(64,80)(65,81)(67,70)(68,86)(69,88)(71,78)(74,75)(76,84)(79,87)(82,85)(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)(54,56,57,55)(59,65)(61,62)(64,75)(66,81)(67,69)(68,82)(70,88)(71,84)(72,77)(74,80)(76,78)(79,83)(85,86)(87,89);(54,55,57,56)(58,59,63,68)(60,70,73,89)(61,65,76,82)(62,67,78,83)(64,79,75,69)(66,84,86,72)(71,88,77,87)(74,81,80,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=fh,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,d^b=dg,e^b=egh,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,g^c=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86235);