Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#1977 ⋊ C2 |
| Sylow | C53 ⋊ #21249 |
1562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 points:
(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)(61,70)(65,73)(68,69)(71,72);(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)(58,61,62,71,64,70,63,72)(59,65,67,69,66,73,60,68);(54,56,57,55)(58,60,63,66,64,67,62,59)(61,68,72,73,70,69,71,65);(54,55,57,56)(58,59,63,67,64,66,62,60)(61,69,72,73,70,68,71,65)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,e^b=eh,g^b=gh,d^c=dh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 173578);