Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2082 ⋊ C2 |
| Sylow | C53 ⋊ #24989 |
620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(54,58,60,81,61,82,59,80)(55,64,66,91,67,92,65,79)(56,70,72,100,73,101,71,99)(57,76,83,109,78,108,77,107)(62,85,86,111,87,98,68,95)(63,89,93,113,90,106,74,104)(69,96,102,117,75,105,97,116)(84,110,103,115,88,112,94,114);(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)(54,57)(55,63)(56,69)(58,76)(59,77)(60,83)(61,78)(62,84)(64,89)(65,74)(66,93)(67,90)(68,94)(70,96)(71,97)(72,102)(73,75)(79,104)(80,107)(81,109)(82,108)(85,110)(86,103)(87,88)(91,113)(92,106)(95,114)(98,112)(99,116)(100,117)(101,105)(111,115);(54,56,60,72,61,73,59,71)(55,62,66,86,67,87,65,68)(57,75,77,102,78,69,83,97)(58,70,81,100,82,101,80,99)(63,88,74,103,90,84,93,94)(64,85,91,111,92,98,79,95)(76,105,107,117,108,96,109,116)(89,112,104,115,106,110,113,114);(54,55,61,67)(56,68,73,86)(57,74,78,93)(58,79,82,91)(59,66,60,65)(62,72,87,71)(63,83,90,77)(64,81,92,80)(69,88,75,84)(70,98,101,85)(76,106,108,89)(94,102,103,97)(95,100,111,99)(96,115,105,114)(104,109,113,107)(110,116,112,117)Polycyclic presentation:
2^8,53|a^2=h,b^2=f,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,g^b=gh,f^c=fh,i^c=i^52,i^d=i^52638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 214699);