Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1953 ⋊ C2 |
| Sylow | C53 ⋊ #13468 |
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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)(58,80)(59,79)(60,87)(61,82)(62,89)(64,97)(65,94)(66,76)(67,100)(68,96)(69,102)(71,77)(72,106)(73,108)(74,110)(75,105)(78,83)(81,85)(84,113)(86,95)(88,103)(90,112)(91,117)(92,116)(93,98)(99,111)(101,104)(107,115)(109,114);(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)(54,56,58,71,60,74,83,88,61,75,84,72,85,101,59,73)(55,62,64,69,67,91,66,90,68,92,65,98,86,107,99,109)(57,77,78,105,81,108,80,110,82,106,79,70,87,103,113,104)(63,93,76,89,95,112,97,115,96,102,111,116,100,114,94,117);(54,55,60,86,61,68,85,67)(56,69,101,90,75,98,74,109)(57,76,87,97,82,111,81,94)(58,66,83,64,84,99,59,65)(62,88,91,71,92,73,107,72)(63,80,95,78,96,113,100,79)(70,89,104,117,105,116,110,115)(77,112,108,93,106,114,103,102)Polycyclic presentation:
2^8,53|a^2=de,b^2=d,d^2=g,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fg,g^a=gh,c^b=cf,e^b=eh,i^b=i^52,d^c=dg,e^c=egh,f^c=fg,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, 89276);