Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#24988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#472×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,7)(3,11)(4,16)(5,17)(9,24)(10,21)(14,15)(18,29)(19,23)(22,30)(25,27)(26,32)(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);(1,2,5,7,6,10,17,21)(3,12,11,19,15,8,14,23)(4,9,16,20,18,24,29,31)(13,26,25,30,28,22,27,32);(1,3)(2,8)(4,13)(5,14)(6,15)(7,19)(9,22)(10,12)(11,17)(16,27)(18,28)(20,30)(21,23)(24,26)(25,29)(31,32);(1,4,17,29,6,18,5,16)(2,9,21,31,10,24,7,20)(3,13,11,25,15,28,14,27)(8,22,23,32,12,26,19,30)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17976);