Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12067 |
246 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 246 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) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 77 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)(54,56,57,61,58,55,59,60)(63,68,71,70)(64,74)(67,69,72,77)(73,75);(63,67)(64,73)(65,76)(68,69)(70,77)(71,72)(74,75);(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)(54,55,57,60,58,56,59,61)(62,63,65,68,66,71,76,70)(64,72,75,69,74,67,73,77)Polycyclic presentation:
2^8,53|a^2=e,c^2=efh,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,i^a=i^52,d^b=dfh,e^b=eh,f^b=fh,d^c=dh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81453);