Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C22 |
| direct product | C73×#10505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C23×C73 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(3,5)(4,7)(6,8)(9,10,14,18)(11,16,20,24)(12,21,19,15)(13,23,22,17)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(3,8)(5,6)(9,11,14,20)(10,15,18,21)(12,22,19,13)(16,17,24,23);(2,5)(3,8)(6,7)(9,12,13,11,14,19,22,20)(10,16,17,21,18,24,23,15)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 3493);