Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#32846 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ #376×C73 ◁ G | |
556 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,4,6)(3,5,7,8)(9,10)(11,15)(12,16)(13,14)(17,23)(18,21)(19,22)(20,24)(25,26)(27,30)(28,32)(29,31)(33,37)(34,39)(35,38)(36,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3)(2,5)(4,7)(6,8)(10,14)(12,19)(15,21)(17,20)(25,27,29,35)(26,30,31,38)(28,33,36,34)(32,37,40,39);(2,6)(5,8)(9,11,13,18)(10,15,14,21)(12,20,19,17)(16,24,22,23)(27,33)(28,36)(30,37)(32,40)(34,35)(38,39);(3,7)(5,8)(9,12,13,19)(10,16,14,22)(11,17,18,20)(15,23,21,24)(26,31)(30,38)(32,40)(37,39)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25834);