Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#25691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#41×C73 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
920 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,4,5)(3,7,8,6)(9,10,15,19)(11,16,22,33)(12,23,25,36)(13,27,14,18)(17,29,35,26)(20,34,37,40)(21,32,28,31)(24,39,38,30)(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);(2,5)(6,7)(9,11)(10,16)(12,24)(13,21)(14,28)(15,22)(17,34)(18,31)(19,33)(20,26)(23,39)(25,38)(27,32)(29,37)(30,36)(35,40);(9,12,13,26,15,25,14,29)(10,17,18,23,19,35,27,36)(11,20,21,38,22,37,28,24)(16,30,31,34,33,39,32,40);(1,3,4,8)(2,6,5,7)(12,25)(17,35)(20,37)(23,36)(24,38)(26,29)(30,39)(34,40)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18679);