Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#32792 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C24×C73 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G | |
600 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)(3,5)(4,6)(7,8)(9,10,14,17)(11,18,12,15)(13,16,21,24)(19,23,20,22)(25,26)(27,30)(28,32)(29,31)(33,37)(34,39)(35,38)(36,40)(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)(4,7)(6,8)(9,11,14,12)(10,15,17,18)(13,20,21,19)(16,23,24,22)(25,27)(26,30)(28,33)(29,35)(31,38)(32,37)(34,36)(39,40);(2,6)(5,8)(9,12,14,11)(10,15,17,18)(13,19,21,20)(16,23,24,22)(27,33)(28,36)(30,37)(32,40)(34,35)(38,39);(3,7)(5,8)(9,13,14,21)(10,16,17,24)(11,19,12,20)(15,22,18,23)(26,31)(30,38)(32,40)(37,39)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25780);