Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1394 ⋊ C2 |
| Sylow | C53 ⋊ #13058 |
668 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 73 points:
(5,7,10,9)(6,12,15,20)(8,18,17,16)(11,19,13,14)(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)(69,70)(71,72);(1,3,4,2)(6,11)(7,9)(8,17)(12,14)(13,15)(19,20)(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)(70,71)(72,73);(1,2,4,3)(5,6,9,11,10,15,7,13)(8,14,16,20,17,19,18,12)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=h,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=egh,g^a=gh,c^b=ch,d^b=dh,e^b=egh,f^b=fh,i^b=i^52,d^c=dg,e^c=eh,f^c=fg,i^c=i^52,e^d=eh,f^e=fh716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86924);