Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×#2029 ⋊ C2 |
| Sylow | C53 ⋊ #32873 |
854 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 4 generators on 69 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)(63,69)(67,68);(54,57)(55,60,61,65)(56,63)(58,66)(59,67,62,68)(64,69);(54,56)(55,59,61,62)(57,63)(58,64)(60,68,65,67)(66,69);(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)(56,62)(57,65)(58,61)(59,64)(60,66)(63,68)(67,69)Polycyclic presentation:
2^8,53|b^2=g,c^2=g,b^a=be,c^a=cf,g^a=gh,i^a=i^52,c^b=cg,d^b=def,e^b=eh,f^b=fh,d^c=de,f^c=fh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 318183);