Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ C4×#362 |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(54,56,57,55);(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)(58,60,61,71,74,85,81,86,62,70,75,69,63,72,76,87)(59,64,65,79,77,83,89,84,66,78,82,68,67,80,73,88);(54,55,57,56)(58,59,62,66)(60,68,70,79)(61,73,75,89)(63,77,74,67)(64,71,78,69)(65,81,82,76)(72,88,85,84)(80,86,83,87)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=eh,d^2=gh,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,d^b=dh,i^c=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84825);