Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#33791 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C73×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G | |
574 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)(3,7)(4,6)(5,8)(10,16)(11,20)(12,15)(14,27)(17,31)(19,36)(21,33)(22,39)(23,38)(25,26)(28,29)(30,35)(32,40)(34,37)(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);(1,3,4,8)(2,5,6,7)(9,10)(11,21)(12,24)(13,16)(14,19)(15,18)(17,23)(20,31)(22,32)(25,36)(26,30)(27,35)(28,40)(29,34)(33,38)(37,39);(3,8)(5,7)(9,11)(10,17)(12,22)(13,23)(14,28)(15,29)(16,21)(18,32)(19,37)(20,27)(24,34)(25,38)(26,39)(30,40)(31,36)(33,35);(2,6)(5,7)(9,12,13,15)(10,18,16,24)(11,22,23,29)(14,25,26,27)(17,32,21,34)(19,35,30,36)(20,28,38,39)(31,37,33,40)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26779);