Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #33426 |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 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)(56,66)(60,65)(67,69)(68,81)(73,75)(74,79)(82,83)(84,85);(55,61,62,64)(57,70)(60,73,65,75)(63,80,78,77)(67,69)(71,76)(74,85,79,84)(82,83);(54,56)(55,60)(57,69)(58,68)(59,66)(61,73)(62,65)(63,79)(64,75)(67,70)(71,83)(72,81)(74,78)(76,82)(77,85)(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)(54,55,57,63,58,64,71,80,59,62,70,78,72,61,76,77)(56,65,67,79,68,73,82,84,66,60,69,74,81,75,83,85)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,f^2=g,g^2=h,b^a=be,c^a=cg,e^a=eh,i^a=i^52,d^b=dh,f^b=fh,f^c=fh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322701);