Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22 |
| direct product | C73×#13269 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #391 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| socle | C2×C73 | #1985 |
| prime radical | C23×C73 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C8×C73 ◁ G | |
308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,7,3,6,11,24,15,8,12,25,16,5,10,23,14)(4,17,20,29,19,9,26,13,21,27,31,18,22,28,32,30)(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);(1,3,7,10,6,15,24,2,8,16,25,11,5,14,23,12)(4,18,31,28,19,30,32,17,21,29,20,9,22,13,26,27);(1,4,6,19,8,21,5,22)(2,9,10,17,12,28,11,27)(3,13,14,29,16,30,15,18)(7,20,24,26,25,31,23,32)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6257);