Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#21676 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C73 | C23 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle, prime radical | C23×C73 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C73 ◁ G | |
658 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)(3,7)(4,8)(5,6)(9,10)(11,13)(12,14)(15,16)(17,18,23,26,22,25,20,21)(19,27,28,29,30,24,31,32)(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);(2,6)(7,8)(9,11,12,15)(10,13,14,16)(17,19)(18,24)(20,31)(21,29)(22,30)(23,28)(25,27)(26,32);(1,3,5,4)(2,7,6,8)(10,14)(13,16)(17,20,22,23)(18,21,25,26)(19,28,30,31)(24,32,27,29);(1,4,5,3)(2,8,6,7)(17,21,20,25,22,26,23,18)(19,29,31,27,30,32,28,24)6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 14664);