Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#28941 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | #537×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2)(3,8)(4,6)(5,7)(9,10)(11,21)(12,25)(13,16)(14,19)(15,20)(17,22)(18,27)(23,37)(24,30)(26,31)(28,34)(29,32)(33,39)(35,36)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3,5,4)(2,6,7,8)(10,16,20,19)(11,22,24,29)(12,26)(17,32)(18,25,34,31)(21,30)(23,38,39,36)(27,28);(1,4,5,3)(2,6,7,8)(9,11,13,22,15,24,14,29)(10,17,19,21,20,32,16,30)(12,23,27,36,26,39,28,38)(18,33,25,35,34,37,31,40);(2,7)(6,8)(9,12,14,28,15,26,13,27)(10,18,16,31,20,34,19,25)(11,23,29,38,24,39,22,36)(17,33,30,40,32,37,21,35)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 21929);