Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C27 |
| direct product | C73×#23889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
1648 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)(7,17)(8,22)(9,16)(10,15)(11,20)(12,24)(13,23)(14,27)(18,33)(19,28)(21,30)(25,32)(26,29)(31,35)(34,36)(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);(5,7,10,21)(6,11,15,29)(8,19,24,34)(9,26,27,20)(12,31,22,33)(13,28,32,36)(14,30,16,17)(18,23,35,25);(2,4)(5,8)(6,12)(7,18)(9,23)(10,24)(11,28)(13,14)(15,22)(16,32)(17,31)(19,26)(20,34)(21,35)(25,27)(29,36)(30,33);(5,8)(6,13)(7,19)(9,25)(10,24)(11,28)(12,14)(15,32)(16,22)(17,33)(18,26)(20,35)(21,34)(23,27)(29,36)(30,31)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16877);