Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#23838 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle, prime radical | C23×C73 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ C43×C73 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2,5,8)(3,7,4,6)(9,10,13,16)(11,15,12,14)(18,21)(22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,3,5,4)(2,6,8,7)(9,11,13,12)(10,14,16,15)(18,22)(20,23)(21,24);(1,3,5,4)(2,7,8,6)(9,12,13,11)(10,15,16,14)(17,18)(19,21)(20,24)(22,23);(1,4,5,3)(2,6,8,7)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16826);