Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25×C4 |
| direct product | C73×#25806 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#578×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
1402 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)(5,6,11,16)(7,13,19,27)(8,20,23,34)(9,24,10,15)(12,25,28,18)(14,22,30,21)(17,31,33,26)(29,35,36,32)(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);(5,7,10,25,11,19,9,18)(6,12,24,27,16,28,15,13)(8,17,22,35,23,33,21,32)(14,26,34,36,30,31,20,29);(1,2,3,4)(5,7)(6,13)(8,17)(9,18)(10,25)(11,19)(12,24)(14,29)(15,28)(16,27)(20,31)(21,32)(22,35)(23,33)(26,34)(30,36);(5,8,10,22,11,23,9,21)(6,14,24,34,16,30,15,20)(7,17,25,35,19,33,18,32)(12,26,27,36,28,31,13,29)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18794);