Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2434 ⋊ C2 |
| Sylow | C53 ⋊ #18261 |
1192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
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)(62,66,68,64)(63,71,72,74)(65,73,67,75)(69,70,77,76);(54,56)(55,58)(57,60)(59,61)(62,65,68,67)(63,70,72,76)(64,73,66,75)(69,74,77,71);(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)(56,58)(57,59)(60,61)(62,64,68,66)(63,69,72,77)(65,73,67,75)(70,74,76,71);(58,61)(62,63,68,72)(64,71,66,74)(65,70,67,76)(69,75,77,73)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 143142);