Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C27 |
| direct product | C73×#23440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#575×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
1898 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)(11,14)(12,19)(13,24)(18,33)(20,28)(21,29)(23,30)(25,31)(26,32)(27,35)(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);(2,4)(5,7)(6,12)(8,23)(9,20)(10,19)(11,21)(13,30)(14,28)(15,29)(16,17)(18,25)(22,33)(24,35)(26,34)(27,32)(31,36);(5,8,11,26)(6,13,14,31)(7,18,21,35)(9,25,10,24)(12,27,28,33)(15,32,16,22)(17,30,29,36)(19,23,20,34);(6,14)(12,28)(13,31)(15,16)(17,29)(22,32)(27,33)(30,36)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16428);