Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C8 |
| direct product | C73×#19703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | #532×C73 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,6,9)(3,10,8,5)(4,7,12,14)(11,16,15,13)(17,18,21,24)(19,25,26,32)(20,28,29,23)(22,30,31,27)(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);(1,3,5,2,6,8,10,9)(4,11,13,7,12,15,16,14)(19,26)(22,31)(25,32)(27,30);(1,4)(2,7)(3,11)(5,13)(6,12)(8,15)(9,14)(10,16)(17,19,20,27,21,26,29,30)(18,22,23,25,24,31,28,32);(4,12)(7,14)(11,15)(13,16)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12691);