Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #8754 |
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)(54,56,57,61)(55,58,59,60)(62,65)(63,69,70,76)(64,73)(66,78)(67,77)(68,81,72,87)(71,84,85,90)(74,89)(75,88)(79,91)(80,83)(82,92,86,93);(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)(62,64,67,75)(63,68,70,72)(65,73,77,88)(66,79,80,74)(69,81,76,87)(71,86,85,82)(78,91,83,89)(84,93,90,92);(54,55)(56,60,61,58)(57,59)(62,63,66,71,67,70,80,85)(64,72,74,86,75,68,79,82)(65,76,78,90,77,69,83,84)(73,81,89,92,88,87,91,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=dh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,i^b=i^52,e^c=eg,f^c=fh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63092);