Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#19863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3303 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,6)(4,12)(7,13)(8,9)(10,16)(14,15)(17,18,22,25)(19,23,21,29)(20,27,28,31)(24,30,32,26)(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);(1,2,5,9)(3,7,11,15)(4,8,12,6)(10,14,16,13)(17,19,22,21)(18,23,25,29)(20,26,28,30)(24,31,32,27);(1,3,5,11)(2,7,9,15)(4,10,12,16)(6,13,8,14)(17,20)(18,24)(19,26)(21,30)(22,28)(23,31)(25,32)(27,29);(2,8)(4,12)(6,9)(7,14)(10,16)(13,15)(17,19,22,21)(18,23,25,29)(20,26,28,30)(24,31,32,27)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12851);