Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2161 ⋊ C2 |
| Sylow | C53 ⋊ #12924 |
386 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 109 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) = 1696 |
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)(57,71)(62,80)(65,81)(66,83)(69,84)(70,85)(72,73)(79,82);(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)(54,56,58,68,60,67,59,75)(55,61,63,77,64,76,74,78)(57,70,72,83,71,85,73,66)(62,79,69,65,80,82,84,81);(54,55,58,63,60,64,59,74)(56,65,68,82,67,81,75,79)(57,69,72,80,71,84,73,62)(61,70,77,83,76,85,78,66)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,e^b=eh,g^b=gh,d^c=dh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86092);