Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#13215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1961 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C73×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2)(3,14)(4,19,23,28)(5,17)(6,11)(7,13)(8,12)(9,22,27,25)(10,15)(16,21,26,31)(18,24)(20,29,32,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,15,13,6,18,24,11,7,10,14,2,8,17,5,12)(4,20,29,28,22,26,21,27,23,32,30,19,25,16,31,9);(1,4,7,23)(2,9)(3,16)(5,21,24,31)(6,22,8,25)(10,26)(11,19)(12,28)(13,27)(14,29,15,30)(17,32)(18,20)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6203);