Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1738 ⋊ C2 |
| Sylow | C53 ⋊ #23522 |
1326 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)(59,66)(64,80)(65,72)(67,76)(68,83)(79,81)(82,87)(84,85);(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)(55,57)(58,61,62,74,63,75,78,89)(59,65,67,82,66,72,76,87)(60,69,70,86,71,73,77,88)(64,79,68,84,80,81,83,85);(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)(58,60,63,71)(59,64,66,80)(61,73,75,69)(62,77,78,70)(65,81,72,79)(67,83,76,68)(74,86,89,88)(82,84,87,85);(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)(54,55)(56,57)(58,59)(60,68)(61,72)(62,76)(63,66)(64,70)(65,75)(67,78)(69,85)(71,83)(73,84)(74,82)(77,80)(79,88)(81,86)(87,89)Polycyclic presentation:
2^8,53|b^2=h,c^2=e,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,i^b=i^52,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197393);