Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#13036 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1879 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#509×C73 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,7,12,14,17,6,11,9,13,25,26,8,3,5,16)(4,18,21,10,27,28,19,15,23,31,24,30,22,32,20,29)(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);(1,3,14,13,9,17,8,2)(4,15,22,30,23,29,27,10)(5,16,7,26,6,11,25,12)(18,21,28,20,31,24,32,19);(1,4)(2,10)(3,15)(5,24)(6,21)(7,19)(8,27)(9,23)(11,28)(12,31)(13,30)(14,22)(16,32)(17,29)(18,26)(20,25)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6024);