Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#26848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | #535×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
718 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)(11,22)(12,27)(13,31)(14,33)(15,20)(16,21)(17,25)(18,29)(19,32)(23,39)(24,38)(26,35)(28,40)(30,37)(34,36)(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)(9,11,14,25,16,26,15,34)(10,17,20,22,21,36,33,35)(12,28,29,23,30,13,24,32)(18,31,27,39,38,40,37,19);(1,4,5,3)(2,6,7,8)(9,12,14,29,16,30,15,24)(10,18,20,27,21,38,33,37)(11,23,25,13,26,32,34,28)(17,19,22,31,36,39,35,40);(2,7)(6,8)(9,13,14,32,16,28,15,23)(10,19,20,31,21,39,33,40)(11,24,25,12,26,29,34,30)(17,18,22,27,36,38,35,37)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 19836);