Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #33337 |
1128 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)(56,64)(61,70)(65,76)(66,77)(73,80)(74,81)(78,84)(83,85);(54,56)(55,61)(57,65)(58,66)(59,64)(60,70)(62,73)(63,74)(67,76)(68,78)(69,77)(71,80)(72,81)(75,83)(79,84)(82,85);(55,60)(57,67)(61,70)(63,72)(65,76)(68,79)(74,81)(78,84);(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)(54,55,57,62,58,63,68,75,59,60,67,71,69,72,79,82)(56,61,65,73,66,74,78,83,64,70,76,80,77,81,84,85)Polycyclic presentation:
2^8,53|a^2=f,f^2=g,g^2=h,b^a=be,e^a=eh,i^a=i^52,f^b=fh,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322262);