Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #8547 |
2486 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 2486 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,3)(2,5)(4,8)(6,7)(17,18,21,26,35,48,65,50,33,45,60,76,85,89,88,83,71,55,42,31,40,53,70,78,58,41,28,19,23,30,39,52,69,82,67,46,62,79,61,77,86,81,68,51,38,29,22,27,36,49,66,74,54,37,24,32,43,56,72,84,87,80,63,75,59,44,57,73,64,47,34,25,20);(10,13)(11,15);(1,2)(3,7,8,5)(4,6)(9,10,11,14,12,13,15,16)(18,19,20,22)(21,24,25,31)(23,28,29,27)(26,33,34,44)(30,37,38,40)(32,41,42,36)(35,46,47,61)(39,50,51,57)(43,54,55,53)(45,58,59,49)(48,63,64,76)(52,67,68,77)(56,65,71,73)(60,74,75,70)(62,78,79,66)(69,80,81,85)(72,82,83,86)(84,87,88,89)Polycyclic presentation:
2^8,73|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^27,f^b=fg,f^c=fh,i^f=i^721192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1088334);