Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25×C4 |
| direct product | C73×#25751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3500 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
1474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(2,3)(5,6)(7,16)(8,20)(9,14)(10,24)(11,15)(12,18)(13,23)(17,34)(19,28)(21,27)(22,32)(25,29)(26,31)(30,35)(33,36)(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);(1,2,4,3)(5,7,9,18)(6,12,14,16)(8,21,22,36)(10,19,11,25)(13,30,31,34)(15,28,24,29)(17,26,35,23)(20,33,32,27);(5,8,10,23,9,22,11,26)(6,13,15,20,14,31,24,32)(7,17,19,36,18,35,25,21)(12,27,28,30,16,33,29,34);(1,3,4,2)(6,14)(8,22)(12,16)(15,24)(17,35)(21,36)(23,26)(28,29)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18739);