Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#10446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C23×C73 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 3 generators on 113 points:
(1,2)(3,5)(4,7)(6,8)(9,10,14,18)(11,19,22,34)(12,23,26,16)(13,27,29,17)(15,28,31,21)(20,36,24,35)(25,33,40,38)(30,37,32,39)(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);(9,11,14,22)(10,15,18,31)(12,24,26,20)(13,28,29,21)(16,32,23,30)(17,34,27,19)(25,37,40,39)(33,35,38,36);(2,5)(3,8)(6,7)(9,12,13,25,14,26,29,40)(10,16,17,33,18,23,27,38)(11,20,21,37,22,24,28,39)(15,30,19,35,31,32,34,36)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 3434);