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 ⋊ #9240 |
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(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)(54,57,58,64)(55,60,61,67)(56,62,63,68)(59,65,66,69)(70,72)(71,76)(73,81)(74,79)(75,83)(77,85)(78,82)(80,84);(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)(70,71,73,80,74,77,82,75)(72,76,81,84,79,85,78,83);(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)(71,75,77,80)(72,78,79,81)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,d^b=dh,e^b=egh,f^b=fh,i^b=i^52,d^c=dgh,e^c=egh,f^c=fgh,i^c=i^52875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 65885);