Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#32828 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ #376×C73 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,4,6)(3,5,7,8)(9,10)(11,16)(12,14)(13,15)(17,18)(19,22)(20,24)(21,23)(25,29)(26,30)(27,31)(28,32)(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);(1,3)(2,5)(4,7)(6,8)(9,11,13,12)(10,14,15,16)(19,25)(20,27)(22,29)(24,31)(26,28)(30,32);(2,6)(5,8)(10,15)(11,12)(17,19,21,26)(18,22,23,30)(20,28,27,25)(24,32,31,29);(3,7)(5,8)(9,12,13,11)(10,14,15,16)(18,23)(22,30)(24,31)(29,32)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25816);