Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#24987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×AGL(1,ℤ/8)×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,7)(3,11)(4,15)(5,17)(9,24)(10,20)(13,14)(16,28)(18,22)(21,29)(25,26)(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);(1,2,5,7,6,10,17,20)(3,8,11,22,14,23,13,18)(4,9,15,19,16,24,28,30)(12,21,25,31,27,32,26,29);(1,3)(2,8)(4,12)(5,13)(6,14)(7,18)(9,21)(10,23)(11,17)(15,26)(16,27)(19,29)(20,22)(24,32)(25,28)(30,31);(1,4,5,15,6,16,17,28)(2,9,7,19,10,24,20,30)(3,12,13,26,14,27,11,25)(8,21,18,29,23,32,22,31)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17975);