Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#33587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C73×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(2,4)(7,15)(8,18)(9,20)(11,23)(13,28)(14,27)(16,33)(17,32)(19,22)(21,31)(24,35)(25,36)(26,34)(29,30)(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)(5,6)(7,11)(8,13)(9,14)(10,12)(15,23)(16,25)(17,24)(18,28)(19,29)(20,27)(21,26)(22,30)(31,34)(32,35)(33,36);(5,7,10,17)(6,11,12,24)(8,19,21,33)(9,22,20,16)(13,29,26,36)(14,30,27,25)(15,31,32,18)(23,34,35,28);(6,12)(11,24)(13,26)(14,27)(23,35)(25,30)(28,34)(29,36)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26575);