Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#22316 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| 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×C4×C73 ◁ G | |
630 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)(3,6)(4,8)(5,7)(9,10)(11,13)(12,15)(14,16)(17,18,23,19,22,25,21,27)(20,24,28,26,29,32,30,31)(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);(1,3,5,4)(2,6,7,8)(9,11,13,10)(12,15,16,14)(17,19,23,25,22,27,21,18)(20,26,28,32,29,31,30,24);(1,4,5,3)(2,6,7,8)(10,11)(14,15)(17,20,22,29)(18,24,25,32)(19,26,27,31)(21,30,23,28);(9,12,13,16)(10,14,11,15)(17,21,22,23)(18,19,25,27)(20,28,29,30)(24,31,32,26)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15304);