Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C26×C73 ⋊ C4 |
| Sylow | C73 ⋊ #12687 |
2508 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 1168 |
A minimal faithful permutation representation — 3 generators on 85 points:
(2,4)(13,14,17,22,31,44,61,46,29,41,56,72,81,85,84,79,67,51,38,27,36,49,66,74,54,37,24,15,19,26,35,48,65,78,63,42,58,75,57,73,82,77,64,47,34,25,18,23,32,45,62,70,50,33,20,28,39,52,68,80,83,76,59,71,55,40,53,69,60,43,30,21,16);(6,9)(10,11);(1,2)(3,4)(5,6)(7,11,12,9)(8,10)(14,15,16,18)(17,20,21,27)(19,24,25,23)(22,29,30,40)(26,33,34,36)(28,37,38,32)(31,42,43,57)(35,46,47,53)(39,50,51,49)(41,54,55,45)(44,59,60,72)(48,63,64,73)(52,61,67,69)(56,70,71,66)(58,74,75,62)(65,76,77,81)(68,78,79,82)(80,83,84,85)Polycyclic presentation:
2^8,73|a^2=f,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^27,f^b=fg,f^d=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, 1096348);