Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2339 ⋊ C2 |
| Sylow | C53 ⋊ #22860 |
1174 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 77 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)(63,69)(65,73)(67,70)(68,75)(71,77)(74,76);(59,61)(62,64,66,72)(63,68,70,76)(65,71,73,77)(67,74,69,75);(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)(54,56,57,55)(62,63,66,70)(64,68,72,76)(65,69,73,67)(71,75,77,74);(54,55,57,56)(58,59)(60,61)(63,67)(65,73)(68,74)(69,70)(71,77)(75,76)Polycyclic presentation:
2^8,53|a^2=g,b^2=gh,c^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,d^b=de,e^b=eh,i^b=i^52,e^d=eh1358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 189911);