Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#26922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C22×D4×C73 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,4,5)(3,7,8,6)(9,10,13,18,14,19,29,16)(11,20,23,31,24,34,21,15)(12,25,26,33,28,32,27,17)(22,30,36,39,38,40,37,35)(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);(2,5)(6,7)(9,11,14,24)(10,15,19,31)(12,22,28,38)(13,21,29,23)(16,20,18,34)(17,30,33,40)(25,35,32,39)(26,37,27,36);(10,16)(11,21)(13,29)(17,25)(18,19)(20,34)(22,36)(23,24)(26,27)(32,33)(35,39)(37,38);(1,3,4,8)(2,6,5,7)(9,12,14,28)(10,17,19,33)(11,22,24,38)(13,27,29,26)(15,30,31,40)(16,25,18,32)(20,35,34,39)(21,36,23,37)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 19910);