Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7426 |
332 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 37 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 — 2 generators on 69 points:
(1,3)(2,6)(4,13,14,10)(5,11)(7,9,12,16)(8,15)(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)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69);(1,2)(3,9)(4,12)(5,8)(6,10,15,13)(7,14)(11,16)(17,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,b^a=bc,c^a=ce,e^a=eg,f^a=fh,c^b=cf,d^b=defg,f^b=fh,g^b=gh,i^b=i^52,d^c=dg,e^c=eh701 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57146);