Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1394 ⋊ C2 |
| Sylow | C53 ⋊ #12862 |
566 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 87 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)(55,59,58,61)(63,69)(64,73)(65,76)(68,80)(70,72)(71,85)(75,88)(77,78)(81,92)(82,83)(84,86)(91,93);(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)(55,58)(59,61)(62,64)(63,68)(65,74)(66,75)(67,73)(69,83)(70,80)(71,81)(72,82)(76,87)(77,89)(78,90)(79,88)(84,92)(85,91)(86,93);(54,55)(56,59)(57,58)(60,61)(62,63,66,71,67,72,79,86)(64,68,75,81,73,82,88,93)(65,70,77,85,76,69,78,84)(74,80,89,91,87,83,90,92)Polycyclic presentation:
2^8,53|a^2=f,c^2=d,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,i^b=i^52,e^c=eh,f^c=fgh,f^e=fh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85839);