Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7492 |
282 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 2 generators on 69 points:
(1,3,6,2,7,9,14,10)(4,13,15,16,11,12,5,8)(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)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68);(1,2,5,8,7,10,15,16)(3,11,12,6,9,4,13,14)(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=h,e^2=h,f^2=h,b^a=bc,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,c^b=ch,d^b=df,f^b=fh,g^b=gh,i^b=i^52,d^c=dgh,f^c=fh,f^d=fh1022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57329);