Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#18297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#538×C73 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G | |
1084 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,11)(3,12,15,21)(4,9,5,18)(7,10,16,24)(8,19,23,13)(14,26,27,32)(17,25,20,29)(22,30,31,28)(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)(5,19)(6,15)(7,14)(9,21)(10,22)(11,23)(12,18)(16,27)(17,28)(20,30)(24,31)(25,32)(26,29);(1,4,16,20)(2,9,24,29)(3,13,27,30)(5,7,17,6)(8,21,31,26)(10,25,11,18)(12,22,32,23)(14,28,15,19);(2,10)(8,22)(9,25)(11,24)(12,26)(18,29)(21,32)(23,31)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 11285);