Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
980 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(5,6,11,15,12,17,10,16)(7,18,20,13,8,22,21,29)(9,24,25,14,27,31,26,32)(19,28,35,36,23,30,34,33)(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)(5,7,11,20,12,8,10,21)(6,13,15,22,17,29,16,18)(9,23,25,34,27,19,26,35)(14,30,31,33,32,28,24,36);(2,4)(5,8,12,7)(6,13,17,29)(9,23,27,19)(10,21,11,20)(14,28,32,30)(15,18,16,22)(24,36,31,33)(25,35,26,34);(5,9)(6,14)(7,19)(8,23)(10,26)(11,25)(12,27)(13,28)(15,31)(16,24)(17,32)(18,33)(20,35)(21,34)(22,36)(29,30)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18182);