Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #19008 |
786 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)(71,78)(76,91)(77,92)(79,86)(80,94)(90,101)(93,95)(96,97);(54,57)(55,60)(56,62)(58,67)(59,65)(61,69)(63,64)(66,68)(70,73,75,85)(71,77,78,92)(72,81,83,99)(74,88,89,84)(76,90,91,101)(79,95,86,93)(80,96,94,97)(82,100,87,98);(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)(54,56,59,55)(57,62,65,60)(58,61,68,63)(64,67,69,66)(70,72,75,83)(71,76,78,91)(73,81,85,99)(74,87,89,82)(77,90,92,101)(79,94,86,80)(84,100,88,98)(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)(54,55,59,56)(57,64,65,69)(58,63,68,61)(60,67,62,66)(70,71,75,78)(72,80,83,94)(73,77,85,92)(74,86,89,79)(76,87,91,82)(81,97,99,96)(84,95,88,93)(90,100,101,98)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=g,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,i^b=i^52,e^c=eh,f^c=fgh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150911);