Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#33828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C73×#2215 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 113 points:
(2,5)(3,7)(9,10)(11,20)(12,17)(13,16)(14,27)(15,21)(18,26)(19,25)(22,28)(23,30)(24,32)(29,38)(31,36)(33,40)(34,39)(35,37)(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);(1,2)(3,6)(4,5)(7,8)(9,11,12,21)(10,15,17,20)(13,22,24,36)(14,23,25,37)(16,31,32,28)(18,29,33,34)(19,30,27,35)(26,39,40,38);(2,5)(6,8)(10,16)(11,21)(13,26)(14,25)(15,28)(17,32)(18,19)(20,31)(22,38)(24,40)(27,33)(29,35)(30,34)(36,39);(1,3,4,7)(2,6,5,8)(10,17)(11,21)(16,32)(18,33)(19,27)(22,36)(23,37)(38,39)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26816);