Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#24807 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | #525×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(5,6,12,16,11,18,10,17)(7,19,28,15,9,27,21,13)(8,22,24,14,26,32,25,31)(20,30,34,33,23,29,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(1,2)(3,4)(5,7,10,21,11,9,12,28)(6,13,16,19,18,15,17,27)(8,20,24,34,26,23,25,35)(14,29,22,33,31,30,32,36);(2,4)(5,8)(6,14)(7,20)(9,23)(10,24)(11,26)(12,25)(13,29)(15,30)(16,22)(17,32)(18,31)(19,33)(21,34)(27,36)(28,35);(5,9,12,21,11,7,10,28)(6,15,17,19,18,13,16,27)(8,23,25,34,26,20,24,35)(14,30,32,33,31,29,22,36)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17795);