Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1952 ⋊ C2 |
| Sylow | C53 ⋊ #13412 |
430 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 99 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)(54,56,57,55)(59,66)(60,70)(61,76)(62,78)(63,77)(65,82)(67,68)(69,87)(71,74)(72,81)(73,75)(79,80)(84,88)(85,86);(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)(58,60,64,74)(59,65,69,86)(61,75,78,72)(62,70,76,71)(63,81,77,73)(66,83,87,89)(67,84,79,88)(68,82,80,85);(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)(55,56)(58,59)(60,65)(61,66)(62,79)(63,80)(64,69)(67,76)(68,77)(70,88)(71,84)(72,89)(73,82)(74,86)(75,83)(78,87)(81,85)Polycyclic presentation:
2^8,53|b^2=h,c^2=d,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fg,g^a=gh,i^a=i^52,c^b=cf,e^b=eg,f^b=fgh,g^b=gh,i^b=i^52,e^c=eg,f^c=fgh,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88943);