Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1912 ⋊ C2 |
| Sylow | C53 ⋊ #28184 |
764 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)(54,58,60,80,61,81,59,79)(55,64,66,91,67,92,65,78)(56,70,73,101,72,100,71,99)(57,75,82,108,77,107,76,106)(62,84,86,110,85,98,68,94)(63,88,93,113,90,112,89,105)(69,96,102,117,97,115,74,104)(83,109,95,114,103,116,87,111);(54,57)(55,63)(56,69)(58,75)(59,76)(60,82)(61,77)(62,83)(64,88)(65,89)(66,93)(67,90)(68,87)(70,96)(71,74)(72,97)(73,102)(78,105)(79,106)(80,108)(81,107)(84,109)(85,103)(86,95)(91,113)(92,112)(94,111)(98,116)(99,104)(100,115)(101,117)(110,114);(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)(54,56,60,73,61,72,59,71)(55,62,66,86,67,85,65,68)(57,74,76,97,77,102,82,69)(58,70,80,101,81,100,79,99)(63,87,89,103,90,95,93,83)(64,84,91,110,92,98,78,94)(75,104,106,115,107,117,108,96)(88,111,105,116,112,114,113,109);(54,55,61,67)(56,68,72,86)(57,63,77,90)(58,78,81,91)(59,66,60,65)(62,73,85,71)(64,80,92,79)(69,95,97,87)(70,98,100,84)(74,103,102,83)(75,105,107,113)(76,93,82,89)(88,108,112,106)(94,101,110,99)(96,109,115,116)(104,114,117,111)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,d^2=eh,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,g^a=gh,c^b=cg,f^b=fh,i^b=i^52,g^c=gh,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 257968);