Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1664 ⋊ C2 |
| Sylow | C53 ⋊ #19013 |
810 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)(54,56,58,63)(55,60,61,67)(57,62,64,68)(59,66,65,69)(70,74,76,75)(71,79,81,80)(72,84,85,88)(73,86,87,89)(77,82,91,94)(78,92,93,95)(83,98,100,99)(90,96,101,97);(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)(56,60)(57,65)(58,61)(59,64)(62,69)(63,67)(66,68)(70,73)(71,78)(72,83)(74,86)(75,89)(76,87)(77,90)(79,92)(80,95)(81,93)(82,96)(84,98)(85,100)(88,99)(91,101)(94,97);(57,64)(59,65)(62,68)(66,69)(70,72,76,85)(71,77,81,91)(73,83,87,100)(74,84,75,88)(78,90,93,101)(79,82,80,94)(86,98,89,99)(92,96,95,97);(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)(55,59)(57,64)(60,66)(61,65)(62,68)(67,69)(70,71,76,81)(72,82,85,94)(73,78,87,93)(74,80,75,79)(77,88,91,84)(83,97,100,96)(86,95,89,92)(90,98,101,99)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,d^2=h,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fgh,i^a=i^52,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^c=i^52,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150978);