Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2117 ⋊ C2 |
| Sylow | C53 ⋊ #12979 |
456 conjugacy classes of subgroups.
| 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)(56,68)(58,77)(59,79)(60,74)(61,73)(62,82)(64,90)(65,92)(66,72)(67,87)(69,99)(70,101)(71,96)(75,81)(76,97)(78,105)(80,86)(83,103)(84,112)(85,109)(88,94)(89,95)(91,104)(93,107)(98,102)(100,114)(106,108)(110,113)(111,116)(115,117);(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)(54,56,59,70,60,69,80,100,61,71,81,102,58,76,78,106)(55,62,65,84,66,83,93,111,67,85,94,113,64,89,91,115)(57,68,79,101,74,99,86,114,73,96,75,98,77,97,105,108)(63,82,92,112,72,103,107,116,87,109,88,110,90,95,104,117);(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)(54,55,59,65,60,66,80,93,61,67,81,94,58,64,78,91)(56,62,70,84,69,83,100,111,71,85,102,113,76,89,106,115)(57,72,75,104,74,87,105,92,73,90,79,107,77,63,86,88)(68,95,98,116,99,82,108,110,96,103,101,117,97,109,114,112)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,e^b=eh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86441);