Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#13247 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #1972 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#509×C73 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ #405×C73 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,7,12)(3,5,11,23)(4,16)(6,25,24,10)(8,15,22,13)(9,26)(14,21)(17,20)(18,27)(19,28)(29,30)(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);(1,3,6,13,8,10,5,12,7,11,24,15,22,25,23,2)(4,17,26,9,20,16,30,27,21,31,19,28,32,14,18,29);(1,4,6,19,8,20,5,18,7,21,24,26,22,32,23,30)(2,9,11,16,13,27,25,31,12,28,3,14,15,29,10,17)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6235);