Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#7845 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C73 | C23 |
| commutator | C22 | C43×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| socle, prime radical | C23×C73 | C2×C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C73 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 109 points:
(5,6,8,12,9,11,15,18)(7,10,14,16,13,17,19,20)(21,22)(23,26)(24,28)(25,27)(29,33)(30,32)(31,34)(35,36)(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);(5,7)(6,10)(8,14)(9,13)(11,17)(12,16)(15,19)(18,20)(21,23,24,29,25,30,31,35)(22,26,28,33,27,32,34,36);(1,2,3,4)(6,11)(7,13)(12,18)(14,19)(22,27)(26,32)(28,34)(33,36)8176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 833);