Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1899 ⋊ C2 |
| Sylow | C53 ⋊ #21423 |
1162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 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)(54,56,57,60)(55,59,58,61)(65,72)(68,75)(70,76)(73,77);(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)(55,58)(59,61)(62,65,66,72)(63,68,69,75)(64,70,71,76)(67,73,74,77);(62,64)(63,67,69,74)(65,70)(66,71)(68,73,75,77)(72,76);(54,55)(56,59)(57,58)(60,61)(62,63)(64,67,71,74)(65,68)(66,69)(70,73,76,77)(72,75)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=h,d^2=f,b^a=be,c^a=cf,e^a=eh,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, 174927);