Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#32856 |
| 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 | |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 113 points:
(2,3)(6,7)(9,10,13,16)(11,17,19,14)(12,15,21,24)(18,23,20,22)(25,26)(27,34)(28,37)(29,33)(30,32)(31,36)(35,40)(38,39)(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);(1,2,5,3)(4,6,8,7)(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,23,24,22)(27,35)(28,30)(31,39)(32,37)(34,40)(36,38);(1,3,5,2)(4,6,8,7)(12,21)(15,24)(18,20)(22,23)(25,27,29,36)(26,31,33,34)(28,35,30,38)(32,40,37,39);(1,4,5,8)(2,6,3,7)(9,12,13,21)(10,15,16,24)(11,18,19,20)(14,22,17,23)(25,28,29,30)(26,32,33,37)(27,35,36,38)(31,40,34,39)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25844);