Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C2×C4 |
| direct product | C73×#10682 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,4,6)(3,7,8,5)(10,13)(14,15)(17,18,22,23,21,26,20,25)(19,27,30,24,29,32,28,31)(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);(1,3,4,8)(2,5,6,7)(9,10,11,13)(12,14,16,15)(18,23)(20,22)(24,27)(25,26)(28,30)(31,32);(10,14)(12,16)(13,15)(17,19,21,29)(18,24,26,31)(20,30,22,28)(23,27,25,32)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 3670);