Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1323 ⋊ C2 |
| Sylow | C53 ⋊ #12165 |
350 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 59 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(54,56,57,60)(55,58,59,61)(62,64)(63,70)(65,74)(66,80)(67,73)(68,75)(69,82)(71,86)(72,87)(76,89)(77,91)(78,92)(79,90)(81,85)(83,93)(84,88);(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)(56,58)(57,59)(60,61)(62,63,68,72)(64,70,75,87)(65,77,79,88)(66,71,67,81)(69,78,83,76)(73,85,80,86)(74,91,90,84)(82,92,93,89);(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)(58,61)(63,69)(64,73)(65,76)(66,67)(70,84)(71,88)(72,83)(74,90)(75,80)(77,81)(78,79)(82,85)(86,93)(87,91)Polycyclic presentation:
2^8,53|b^2=h,c^2=g,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,i^a=i^52,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh1019 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82050);