Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24×C4 |
| direct product | C73×#25619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C73×#3512 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
1052 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)(3,7)(4,5)(6,8)(9,10)(11,20)(12,24)(13,18)(14,28)(15,19)(16,22)(17,27)(21,38)(23,32)(25,31)(26,36)(29,33)(30,35)(34,39)(37,40)(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);(2,5)(6,7)(9,11)(10,16)(12,25)(13,22)(14,23)(15,29)(17,34)(18,20)(19,32)(21,27)(24,37)(26,40)(28,33)(30,39)(31,36)(35,38);(9,12,14,27,13,26,15,30)(10,17,19,24,18,35,28,36)(11,21,23,40,22,39,29,25)(16,31,32,34,20,37,33,38);(1,3,4,8)(2,6,5,7)(10,18)(12,26)(16,20)(19,28)(21,39)(25,40)(27,30)(32,33)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 18607);