Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9056 |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,56,57,63)(55,60,59,68)(58,67,65,64)(61,69,66,62)(70,72)(71,76)(73,81)(74,79)(75,83)(77,85)(78,82)(80,84);(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)(55,59)(60,68)(61,66)(62,69)(70,71,73,80,74,77,82,75)(72,76,81,84,79,85,78,83);(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)(56,62)(57,59)(58,66)(60,64)(61,65)(63,69)(67,68)(71,75,77,80)(72,78,79,81)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,d^b=dg,e^b=eg,f^b=fg,i^b=i^52,d^c=dg,e^c=egh,f^c=fg1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64812);