Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #9500 |
660 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,57,58,64)(55,60,61,67)(56,62,63,68)(59,65,66,69)(70,73)(71,76)(72,78)(74,81)(75,82)(77,80)(79,84)(83,85);(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)(55,59,61,66)(57,62)(58,63)(60,65,67,69)(64,68)(70,72,74,79)(71,75,77,83)(73,78,81,84)(76,82,80,85);(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)(56,59,63,66)(57,60)(58,61)(62,65,68,69)(64,67)(70,71)(72,75)(73,80,81,76)(74,77)(78,82,84,85)(79,83)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,f^c=fh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 67493);