Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1979 ⋊ C2 |
| Sylow | C53 ⋊ #13035 |
456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 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)(55,63)(56,70)(58,81)(59,77)(60,86)(61,80)(62,88)(64,93)(65,97)(66,76)(67,100)(68,95)(69,101)(71,105)(72,108)(73,104)(74,110)(75,107)(78,83)(79,84)(82,111)(85,106)(87,94)(89,112)(90,116)(91,115)(92,98)(96,117)(99,114)(102,113)(103,109);(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)(54,56,60,85,61,75,84,74)(55,62,87,90,68,91,67,99)(57,70,86,106,80,107,79,110)(58,73,82,71,83,109,59,72)(63,88,94,116,95,115,100,114)(64,96,98,102,65,89,66,69)(76,101,93,117,92,113,97,112)(77,108,81,104,111,105,78,103);(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)(54,55,59,66,84,87,83,64,61,68,82,98,60,67,58,65)(56,69,73,62,85,89,71,99,75,102,109,91,74,96,72,90)(57,76,78,95,86,97,77,94,80,92,81,63,79,93,111,100)(70,88,105,113,110,116,104,112,107,115,108,101,106,114,103,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^52,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,f^c=fgh,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86789);