Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#33876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C4×D4×C73 ◁ C8×D4×C73 ◁ G | |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,20)(12,17)(13,25)(14,29)(15,19)(16,23)(18,27)(21,36)(22,38)(24,35)(26,32)(28,37)(30,34)(31,39)(33,40)(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)(4,8)(6,7)(11,21)(16,31)(20,36)(22,30)(23,39)(26,40)(32,33)(34,38);(9,11,15,21)(10,16,19,31)(12,22,14,30)(13,26,28,40)(17,32,29,33)(18,34,35,38)(20,37,36,25)(23,24,39,27);(3,8)(5,7)(9,12,15,14)(10,17,19,29)(11,22,21,30)(13,24,28,27)(16,32,31,33)(18,25,35,37)(20,38,36,34)(23,26,39,40)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26864);