Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#26851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×AGL(1,ℤ/8)×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
720 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)(3,8)(4,6)(5,7)(9,10)(11,23)(12,29)(13,33)(14,21)(15,20)(16,22)(17,26)(18,31)(19,24)(25,39)(27,36)(28,35)(30,37)(32,38)(34,40)(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);(1,3,5,4)(2,6,7,8)(9,11,15,27,16,28,14,26)(10,17,21,35,22,36,20,23)(12,30,31,24,32,13,25,34)(18,37,29,40,39,33,38,19);(1,4,5,3)(2,6,7,8)(9,12,14,25,16,32,15,31)(10,18,20,38,22,39,21,29)(11,24,26,30,28,34,27,13)(17,19,23,33,36,40,35,37);(2,7)(6,8)(9,13,14,24,16,30,15,34)(10,19,20,33,22,40,21,37)(11,25,26,32,28,31,27,12)(17,18,23,38,36,39,35,29)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 19839);