Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2177 ⋊ C2 |
| Sylow | C53 ⋊ #33830 |
760 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 73 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)(58,60)(59,64)(61,71)(62,69)(63,72)(65,70)(66,68);(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)(55,57);(58,59)(60,67)(61,70)(62,65)(63,66)(64,68)(69,73)(71,72);(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)(54,55)(56,57)(59,63)(60,66)(61,68)(64,73)(65,72)(67,70)(69,71)Polycyclic presentation:
2^8,53|e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,g^a=gh,i^a=i^52,d^b=de,e^b=eg,g^b=gh,i^c=i^52,e^d=eg,g^d=gh875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326028);