Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#2005 ⋊ C2 |
| Sylow | C53 ⋊ #23911 |
1738 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)(58,61,63,59)(60,67,68,64)(62,65,72,70)(66,71,73,69);(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)(55,57)(58,60)(59,64)(61,67)(62,71)(63,68)(65,73)(66,70)(69,72);(54,55)(56,57)(58,59,63,61)(60,64,68,67)(62,70,72,65)(66,69,73,71);(58,59,63,61)(60,66,68,73)(62,70,72,65)(64,71,67,69)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,f^b=fh,e^c=eh,f^c=fh,f^d=fh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201244);