Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #26023 |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 85 points:
(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)(62,64,65,69)(63,67,66,68);(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)(54,56,57,61)(55,58,59,60)(72,78)(73,81)(75,82)(76,85)(79,80)(83,84);(63,66)(67,68)(70,72,74,80)(71,75,77,84)(73,78,81,79)(76,82,85,83);(54,55,57,59)(56,60,61,58)(62,63)(64,68)(65,66)(67,69)(70,71,74,77)(72,75,80,84)(73,76,81,85)(78,82,79,83)Polycyclic presentation:
2^8,53|a^2=fh,b^2=h,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,g^c=gh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 227677);