Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#135×C73 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×C4×C8×C73 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 109 points:
(1,2)(3,4)(5,6)(7,19)(8,26)(9,16)(10,15)(11,28)(12,31)(13,18)(14,21)(17,29)(20,22)(23,35)(24,27)(25,36)(30,34)(32,33)(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);(5,7,13,25)(6,14,18,35)(8,27,15,33)(9,22,11,30)(10,21,26,23)(12,32,29,24)(16,19,28,36)(17,20,31,34);(2,4)(5,8,9,17,29,16,26,6,13,15,11,31,12,28,10,18)(7,20,21,27,32,35,30,36,25,34,23,33,24,14,22,19)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6434);