Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C22×#41×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2)(3,4)(5,6,9,14,11,16,10,15)(7,12,18,27,19,28,25,32)(8,20,22,31,24,30,23,13)(17,29,21,35,33,36,34,26)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(2,4)(5,7)(6,12)(8,21)(9,18)(10,25)(11,19)(13,29)(14,27)(15,32)(16,28)(17,23)(20,35)(22,33)(24,34)(26,30)(31,36);(5,8,11,24)(6,13,16,31)(7,17,19,33)(9,23,10,22)(12,26,28,35)(14,30,15,20)(18,34,25,21)(27,36,32,29);(2,4)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17388);