Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33401 |
684 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)(57,71)(63,77)(68,82)(72,74)(73,83)(76,79)(78,84)(81,85);(54,57)(55,63)(56,68)(58,72)(59,73)(60,74)(61,71)(62,76)(64,78)(65,79)(66,77)(67,81)(69,83)(70,82)(75,84)(80,85);(54,56,58,69,61,70,60,59)(55,62,64,67,66,65,75,80)(57,68,72,83,71,82,74,73)(63,76,78,81,77,79,84,85);(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)(54,55,59,65,60,64,70,80,61,66,69,62,58,75,56,67)(57,63,73,79,74,78,82,85,71,77,83,76,72,84,68,81)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,e^2=h,f^2=g,g^2=h,b^a=be,e^a=eh,i^a=i^52,d^c=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322572);