Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#20152 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#1619 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,7)(3,5)(8,15)(9,13)(10,14)(11,16)(17,18,22,25)(19,26,27,32)(20,24,21,29)(23,30,31,28)(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);(1,2)(3,7)(4,11)(5,13)(6,9)(8,10)(12,15)(14,16)(19,27)(23,31)(26,32)(28,30);(1,3,6,5)(2,7,9,13)(4,10,12,14)(8,15,16,11)(17,19,22,27)(18,23,25,31)(20,28,21,30)(24,32,29,26);(1,4,6,12)(2,8,9,16)(3,10,5,14)(7,15,13,11)(17,20,22,21)(18,24,25,29)(19,28,27,30)(23,32,31,26)2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13140);