Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#1908 ⋊ C2 |
| Sylow | C53 ⋊ #23889 |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,61)(59,67)(60,72)(62,79)(63,76)(64,77)(65,80)(66,78)(68,84)(69,83)(70,82)(71,73)(74,87)(75,88)(81,89)(85,86);(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)(55,57)(58,61)(59,66)(60,71)(62,76)(63,79)(64,77)(65,80)(67,78)(68,83)(69,84)(70,86)(72,73)(74,88)(75,87)(81,89)(82,85);(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)(58,60,64,75)(59,65,69,81)(61,72,77,88)(62,74,63,73)(66,82,84,86)(67,80,83,89)(68,85,78,70)(71,79,87,76);(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)(56,57)(58,59)(60,70)(61,66)(62,78)(63,68)(64,69)(65,73)(67,76)(71,86)(72,80)(74,81)(75,85)(77,84)(79,83)(82,87)(88,89)Polycyclic presentation:
2^8,53|b^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,g^b=gh,i^b=i^52,g^c=gh,i^c=i^52,e^d=eh875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201063);