Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#33471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×#442 |
| commutator | C8 | C23×C4×C73 |
| Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C2×#509×C73 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,12,16,29)(4,18)(5,9)(6,19)(7,11)(8,15,25,32)(10,20)(13,30,24,21)(14,28,17,26)(22,23)(27,31)(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)(2,8)(4,13)(5,14)(6,21)(7,16)(9,24)(10,26)(11,25)(12,22)(15,31)(17,18)(19,29)(20,32)(23,30)(27,28);(1,4,18,2,7,9,5,11)(3,13,17,8,16,24,14,25)(6,22,31,27,23,19,20,10)(12,15,28,30,29,32,26,21);(1,5,7,18)(2,9,11,4)(3,14,16,17)(6,20,23,31)(8,24,25,13)(10,22,27,19)(12,28,29,26)(15,21,32,30)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26459);