Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#9526 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #386 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C23×C4 | C23×C73 |
| prime radical | C24×C73 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,5,9,6,10,4,7)(3,11,13,8,14,15,12,16)(17,18)(19,22)(20,27,28,23)(21,24)(25,29,31,32)(26,30)(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);(2,7,10,9)(8,11,16,15)(17,19,21,26)(18,22,24,30)(20,25,28,31)(23,29,27,32);(1,3,6,14)(2,8,10,16)(4,12,5,13)(7,11,9,15)(17,20)(18,23)(19,25)(21,28)(22,29)(24,27)(26,31)(30,32)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2514);