Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#20035 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 97 points:
(2,5)(3,7)(6,8)(9,10,15,13)(11,18,20,24)(12,17,14,21)(16,23,22,19)(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);(2,6)(5,8)(9,11)(10,16)(12,19)(13,22)(14,23)(15,20)(17,24)(18,21);(1,2)(3,8)(4,6)(5,7)(9,12,15,14)(10,17,13,21)(11,19,20,23)(16,24,22,18);(9,13,15,10)(11,18,20,24)(12,21,14,17)(16,23,22,19)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13023);