Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C53×#2359 ⋊ C2 |
| Sylow | C53 ⋊ #34527 |
2216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 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)(54,56,57,55)(59,63)(64,65);(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)(58,61,62,60)(59,65,63,64)(66,68,69,72)(67,71,70,73);(54,55,57,56)(58,60,62,61)(59,64,63,65)(66,67)(68,71)(69,70)(72,73);(59,63)(60,61)(67,70)(71,73);(54,55,57,56)(58,59)(60,65)(61,64)(62,63)(67,70)(68,72)Polycyclic presentation:
2^8,53|a^2=h,c^2=fh,d^2=g,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^e=i^521376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 335690);