Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1696 ⋊ C2 |
| Sylow | C53 ⋊ #19226 |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 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)(54,57,58,59)(55,62,60,66)(56,64,65,67)(61,69,68,63)(73,85)(77,91)(82,96)(86,95)(89,100)(92,98)(93,101)(97,99);(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)(55,61)(57,64)(58,65)(59,67)(60,68)(62,69)(63,66)(70,73)(71,77)(72,82)(74,86)(75,85)(76,89)(78,92)(79,91)(80,93)(81,95)(83,97)(84,96)(87,98)(88,99)(90,100)(94,101);(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)(55,60)(61,68)(62,66)(63,69)(70,72,81,88,75,84,74,83)(71,76,87,94,79,90,78,80)(73,82,95,99,85,96,86,97)(77,89,98,101,91,100,92,93);(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)(56,63)(57,62)(58,60)(59,66)(61,64)(65,69)(67,68)(70,71,75,79)(72,80,84,94)(73,77,85,91)(74,87,81,78)(76,88,90,83)(82,93,96,101)(86,98,95,92)(89,99,100,97)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,d^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^52,i^b=i^52,d^c=dg,f^c=fh,i^c=i^52,i^d=i^52644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 153007);