Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1379 ⋊ C2 |
| Sylow | C53 ⋊ #13016 |
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 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)(55,64)(56,70)(58,81)(59,86)(60,77)(61,88)(62,80)(63,89)(65,76)(66,93)(67,101)(68,96)(69,102)(71,106)(72,105)(73,109)(74,110)(75,108)(78,83)(79,82)(84,112)(85,113)(87,107)(90,117)(91,104)(92,116)(94,99)(95,98)(97,111)(100,115)(103,114);(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)(54,56,61,87,62,75,82,74)(55,63,67,100,68,92,98,91)(57,70,88,107,80,108,79,110)(58,72,60,71,83,73,59,85)(64,89,101,115,96,116,95,104)(65,97,66,69,99,90,84,103)(76,111,93,102,94,117,112,114)(77,106,78,109,86,113,81,105);(54,55,60,66,61,67,83,99,62,68,59,84,82,98,58,65)(56,69,73,92,74,97,71,100,75,103,72,63,87,90,85,91)(57,76,78,101,79,112,77,64,80,94,81,95,88,93,86,96)(70,104,106,111,107,89,109,102,108,115,113,117,110,116,105,114)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^52,d^c=dg,e^c=egh,f^c=fg,g^c=gh,i^c=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86652);