Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9422 |
384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57,59,66)(55,61,56,64)(58,67,60,65)(62,69,63,68)(70,73,76,86)(71,78,79,94)(72,81,82,97)(74,88,75,85)(77,90,93,100)(80,95,87,84)(83,99,89,98)(91,101,92,96);(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)(54,56,59,55)(57,64,66,61)(58,62,60,63)(65,68,67,69)(70,72,74,83,76,82,75,89)(71,77,80,91,79,93,87,92)(73,81,88,99,86,97,85,98)(78,90,95,101,94,100,84,96);(54,55,60,63,59,56,58,62)(57,61,67,69,66,64,65,68)(70,71,75,80,76,79,74,87)(72,77,83,92,82,93,89,91)(73,84,85,78,86,95,88,94)(81,96,99,100,97,101,98,90)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,d^2=gh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,e^b=egh,f^b=fh,i^b=i^52,d^c=dgh,e^c=eg,f^c=fgh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 67088);