Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#24458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#577×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
1328 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)(7,12)(8,20)(9,11)(10,15)(13,21)(14,24)(16,27)(17,32)(18,25)(19,28)(22,29)(23,30)(26,31)(33,35)(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);(6,11)(7,16)(9,24)(13,20)(14,15)(17,31)(18,19)(21,22)(25,27)(29,30)(32,35)(33,34);(2,4)(5,7,10,19)(6,12,15,28)(8,17,23,33)(9,18,24,16)(11,25,14,27)(13,26,29,36)(20,32,30,35)(21,31,22,34);(5,8)(6,13)(7,17)(9,22)(10,23)(11,20)(12,26)(14,30)(15,29)(16,31)(18,34)(19,33)(21,24)(25,32)(27,35)(28,36)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17446);