Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#13337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#509×C73 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 109 points:
(6,13)(7,19)(8,24)(9,27)(10,11)(14,31)(15,18)(16,25)(17,28)(21,29)(22,26)(23,35)(30,32)(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);(1,2)(3,4)(5,6,12,18)(7,20,23,33)(8,25,9,28)(10,17,11,16)(13,27,15,24)(14,22,31,21)(19,32,35,36)(26,34,29,30);(2,4)(5,7)(6,14)(8,26)(9,29)(10,22)(11,21)(12,23)(13,30)(15,34)(16,33)(17,20)(18,31)(19,27)(24,35)(25,36)(28,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6325);