Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C73 ⋊ #8298 |
2574 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 2574 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 93 points:
(2,4)(21,22,25,30,39,52,69,54,37,49,64,80,89,93,92,87,75,59,46,35,44,57,74,82,62,45,32,23,27,34,43,56,73,86,71,50,66,83,65,81,90,85,72,55,42,33,26,31,40,53,70,78,58,41,28,36,47,60,76,88,91,84,67,79,63,48,61,77,68,51,38,29,24);(13,15)(14,17)(16,20)(18,19);(1,2)(3,4)(5,6,7,9,8,10,11,12)(13,14)(15,19,20,17)(16,18)(22,23,24,26)(25,28,29,35)(27,32,33,31)(30,37,38,48)(34,41,42,44)(36,45,46,40)(39,50,51,65)(43,54,55,61)(47,58,59,57)(49,62,63,53)(52,67,68,80)(56,71,72,81)(60,69,75,77)(64,78,79,74)(66,82,83,70)(73,84,85,89)(76,86,87,90)(88,91,92,93)Polycyclic presentation:
2^8,73|a^2=f,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^27,f^b=fg,i^f=i^721216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1087670);