Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#19054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3150 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 113 points:
(2,5)(3,7)(6,8)(9,10)(11,21)(12,26)(13,18)(14,19)(15,20)(16,24)(17,28)(22,30)(23,31)(25,34)(27,32)(29,33)(35,37)(36,39)(38,40)(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);(3,7)(5,8)(9,11)(10,16)(12,22)(13,23)(14,24)(15,25)(17,30)(18,21)(19,34)(20,31)(26,39)(27,36)(28,37)(29,38)(32,40)(33,35);(1,2)(3,8)(4,6)(5,7)(9,12,15,29)(10,17,20,32)(11,22,25,38)(13,28,14,27)(16,30,31,40)(18,33,19,26)(21,35,34,39)(23,37,24,36);(9,13,15,14)(10,18,20,19)(11,23,25,24)(12,27,29,28)(16,21,31,34)(17,26,32,33)(22,36,38,37)(30,39,40,35)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12042);