Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#19249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | #121×C73 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,10)(3,11,13,15)(4,14,7,8)(5,16,12,9)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32)(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);(1,3,12,8,6,13,5,14)(2,7,16,15,10,4,9,11);(1,4)(2,8)(3,9)(5,15)(6,7)(10,14)(11,12)(13,16)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(3,13)(4,7)(8,14)(11,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12237);