Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #17856 |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(63,70)(65,76)(68,82)(71,78)(72,85)(73,87)(77,89)(88,91);(54,56,57,61,58,55,59,60)(62,65,67,76)(63,69,70,84)(64,73,75,87)(66,77,80,89)(68,81,82,92)(71,83,78,90)(72,86,85,93)(74,88,79,91);(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)(62,64,67,75)(63,68,70,82)(65,73,76,87)(66,79,80,74)(69,81,84,92)(71,85,78,72)(77,91,89,88)(83,93,90,86);(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)(54,55,57,60,58,56,59,61)(62,63)(64,72)(65,69)(66,78)(67,70)(68,74)(71,80)(73,86)(75,85)(76,84)(77,90)(79,82)(81,88)(83,89)(87,93)(91,92)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=fg,e^2=g,f^2=h,b^a=be,d^a=dg,e^a=eg,i^a=i^52,e^b=eg,i^b=i^52,d^c=dg2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 139043);