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 ⋊ #8006 |
542 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68);(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)(55,59)(57,63)(58,64)(60,66)(61,62)(65,69)(67,68)(70,72,74,81,75,82,73,80)(71,76,77,79,78,85,83,84);(54,55)(56,62,64,59)(57,60)(58,61)(63,68,69,66)(65,67)(70,71,73,77,75,78,74,83)(72,79,81,76,82,84,80,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,d^2=gh,e^2=gh,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,e^b=eh,i^c=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 59533);