Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#24927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
862 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)(3,5)(4,6)(7,8)(9,10)(11,16)(12,24)(13,15)(14,19)(17,25)(18,28)(20,31)(21,36)(22,29)(23,32)(26,33)(27,34)(30,35)(37,39)(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);(1,3,4,7)(2,5,6,8)(10,15)(11,20)(13,28)(17,24)(18,19)(21,35)(22,23)(25,26)(29,31)(33,34)(36,39)(37,38);(2,6)(5,8)(9,11,14,23)(10,16,19,32)(12,21,27,37)(13,22,28,20)(15,29,18,31)(17,30,33,40)(24,36,34,39)(25,35,26,38);(9,12)(10,17)(11,21)(13,26)(14,27)(15,24)(16,30)(18,34)(19,33)(20,35)(22,38)(23,37)(25,28)(29,36)(31,39)(32,40)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17915);