Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#18259 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | #525×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
1132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 97 points:
(5,8)(9,10,15,12)(11,19,22,24)(13,18,14,17)(16,23,20,21)(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);(1,2)(3,5)(4,6)(7,8)(9,11)(10,16)(12,20)(13,21)(14,23)(15,22)(17,19)(18,24);(1,3)(2,5)(4,7)(6,8)(9,12,15,10)(11,20,22,16)(13,17,14,18)(19,23,24,21);(9,13,15,14)(10,17,12,18)(11,21,22,23)(16,19,20,24)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 11247);