Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#32863 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C43×C73 ◁ G | |
600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,4,7)(3,6,8,5)(9,10)(11,14)(12,13)(15,16)(18,22)(23,31)(24,29)(25,32)(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)(2,5)(4,8)(6,7)(10,13)(14,16)(17,18,20,22)(19,25,26,32)(21,29,28,24)(23,30,31,27);(1,3)(2,6)(4,8)(5,7)(10,13)(11,15)(17,19,20,26)(18,23,22,31)(21,30,28,27)(24,32,29,25);(3,8)(5,6)(9,11,12,15)(10,14,13,16)(18,22)(19,26)(24,29)(27,30)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 25851);