Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2005 ⋊ C2 |
| Sylow | C53 ⋊ #24415 |
1402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
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)(58,62)(59,61)(60,63)(64,72)(65,70)(66,68)(67,71)(69,73);(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)(58,61)(59,62)(60,68)(63,66)(64,71)(65,69)(67,72)(70,73);(54,55)(56,57)(58,60,64,70)(59,66,67,69)(61,68,71,73)(62,63,72,65);(58,59,65,73,64,67,63,68)(60,69,72,61,70,66,62,71)Polycyclic presentation:
2^8,53|a^2=fh,b^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^b=fh,e^c=eh,f^c=fh,f^d=fh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 207023);