Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #25005 |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
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)(62,64,65,69)(63,67,66,68)(72,79)(75,83)(78,81)(82,85);(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)(55,59)(58,61)(70,72,74,79)(71,75,77,83)(73,81,80,78)(76,85,84,82);(54,56,57,60)(55,58,59,61)(63,66)(67,68)(72,78)(73,80)(75,82)(76,84)(79,81)(83,85);(54,55)(56,58)(57,59)(60,61)(62,63,65,66)(64,68,69,67)(70,71,74,77)(72,75,79,83)(73,76,80,84)(78,82,81,85)Polycyclic presentation:
2^8,53|a^2=eh,b^2=f,c^2=h,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,d^c=dh,g^c=gh,i^c=i^521346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 214902);