Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8699 |
598 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 85 points:
(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)(62,64,65,68)(63,67,66,69)(70,73)(71,76)(72,78)(74,81)(75,82)(77,80)(79,85)(83,84);(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)(63,66)(67,69)(70,72,74,79)(71,75,77,83)(73,78,81,85)(76,82,80,84);(54,55,56,58,57,59,60,61)(62,63)(64,67)(65,66)(68,69)(70,71)(72,75)(73,80,81,76)(74,77)(78,84,85,82)(79,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^c=fg,i^c=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62892);