Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#19881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C2×D4×C73 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
562 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)(7,15)(8,13)(9,16)(10,14)(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);(1,2,5,8)(3,9,11,15)(4,13,12,6)(7,14,16,10)(17,19,22,21)(18,23,25,29)(20,26,28,30)(24,31,32,27);(17,20,22,28)(18,24,25,32)(19,26,21,30)(23,31,29,27);(1,3,5,11)(2,7,8,16)(4,14,12,10)(6,15,13,9)(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, 12869);