Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1394 ⋊ C2 |
| Sylow | C53 ⋊ #12586 |
746 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 151 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(60,69)(64,79)(68,84)(70,86)(71,75)(78,87)(80,89)(85,88);(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)(54,55,56,57)(58,60)(59,64,67,79)(61,70)(62,75)(63,69)(65,68,72,84)(66,80,83,89)(71,77)(73,87)(74,86)(76,78)(81,85,82,88);(58,59,62,66,63,67,77,83)(60,68,71,85,69,84,75,88)(61,72,73,82,74,65,76,81)(64,78,80,86,79,87,89,70)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,d^2=h,e^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^c=i^52,e^d=eh722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84551);