Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1535 ⋊ C2 |
| Sylow | C53 ⋊ #19097 |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57,59,58)(55,61,62,65)(56,63,64,66)(60,68,69,67)(70,74,76,75)(71,79,81,80)(72,84,86,85)(73,87,88,89)(77,91,92,82)(78,93,94,95)(83,98,99,100)(90,97,101,96);(54,56)(55,60)(57,63)(58,66)(59,64)(61,68)(62,69)(65,67)(70,73)(71,78)(72,83)(74,87)(75,89)(76,88)(77,90)(79,93)(80,95)(81,94)(82,96)(84,98)(85,100)(86,99)(91,97)(92,101);(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)(54,55)(56,60)(57,61)(58,65)(59,62)(63,68)(64,69)(66,67)(70,72,76,86)(71,77,81,92)(73,83,88,99)(74,85,75,84)(78,90,94,101)(79,82,80,91)(87,100,89,98)(93,96,95,97);(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)(56,63)(57,58)(60,67)(61,65)(64,66)(68,69)(70,71,76,81)(72,82,86,91)(73,78,88,94)(74,80,75,79)(77,84,92,85)(83,97,99,96)(87,95,89,93)(90,100,101,98)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=dh,e^a=eg,f^a=fgh,i^a=i^52,d^b=dg,e^b=eg,f^b=fh,i^b=i^52,e^c=eh,f^c=fgh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151783);