Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#18250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
932 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)(4,15)(8,19)(9,18)(10,16)(13,23)(17,25)(20,26)(21,29)(22,30)(27,28)(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);(1,2,5,10)(3,8,11,20)(4,16,15,7)(6,9,12,21)(13,26,23,19)(14,22,24,32)(17,29,25,18)(27,30,28,31);(3,11)(4,17)(7,18)(8,20)(13,27)(14,24)(15,25)(16,29)(19,31)(22,32)(23,28)(26,30);(1,3,12,24)(2,8,21,32)(4,13,25,27)(5,11,6,14)(7,19,29,31)(9,22,10,20)(15,23,17,28)(16,26,18,30)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 11238);