Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12608 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,56,57,55)(59,66)(60,71,73,72)(62,76)(65,70,78,81)(67,69)(74,86,87,85)(75,77)(79,89,88,84);(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)(58,60,62,74,63,72,77,86,64,73,76,87,61,71,75,85)(59,65,68,79,69,70,83,84,66,78,80,88,67,81,82,89);(54,55,57,56)(58,59)(60,70,73,81)(61,67)(62,68)(63,69)(64,66)(65,72,78,71)(74,84,87,89)(75,82)(76,80)(77,83)(79,86,88,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ch,c^b=cg,d^b=dh,e^b=eh,i^b=i^52,f^c=fh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84638);