Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1521 ⋊ C2 |
| Sylow | C53 ⋊ #8514 |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(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)(55,62)(56,67)(58,73)(59,71)(60,72)(61,74)(63,79)(64,77)(65,78)(66,80)(68,84)(69,83)(70,82)(75,85)(76,81)(86,89)(87,93)(88,97)(90,105)(91,101)(92,107)(94,109)(95,111)(96,112)(98,116)(99,114)(100,103)(102,106)(104,115)(108,113)(110,117);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56)(55,61)(57,67)(58,70)(59,68)(60,69)(62,74)(63,76)(64,66)(65,75)(71,84)(72,83)(73,82)(77,80)(78,85)(79,81)(86,88)(87,92)(89,97)(90,104)(91,99)(93,107)(94,96)(95,110)(98,106)(100,113)(101,114)(102,116)(103,108)(105,115)(109,112)(111,117);(54,55,59,64,60,65,58,63)(56,66,70,61,69,76,68,75)(57,62,71,77,72,78,73,79)(67,81,82,85,83,80,84,74)(86,87)(88,96,99,92)(89,100)(90,103)(91,94)(93,102)(95,106)(97,113,114,117)(98,108,104,110)(101,111)(105,109)(107,115,112,116)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,e^c=eg,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62053);