Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#22625763 |
| Sylow | C73 ⋊ C2×#1783 |
5942 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 87 points:
(4,6)(15,16,19,24,33,46,63,48,31,43,58,74,83,87,86,81,69,53,40,29,38,51,68,76,56,39,26,17,21,28,37,50,67,80,65,44,60,77,59,75,84,79,66,49,36,27,20,25,34,47,64,72,52,35,22,30,41,54,70,82,85,78,61,73,57,42,55,71,62,45,32,23,18);(8,11)(9,13);(3,4)(5,6)(7,8,9,12,10,11,13,14)(16,17,18,20)(19,22,23,29)(21,26,27,25)(24,31,32,42)(28,35,36,38)(30,39,40,34)(33,44,45,59)(37,48,49,55)(41,52,53,51)(43,56,57,47)(46,61,62,74)(50,65,66,75)(54,63,69,71)(58,72,73,68)(60,76,77,64)(67,78,79,83)(70,80,81,84)(82,85,86,87);(1,2)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1104418);