Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#26404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#41×C73 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,5,7)(3,6,4,8)(9,10)(11,21)(12,16)(13,19)(14,20)(15,24)(17,26)(18,30)(22,35)(23,32)(25,33)(27,36)(28,37)(29,34)(31,38)(39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3,5,4)(2,6,7,8)(9,11,14,25)(10,15,20,34)(12,23,28,38)(13,29,30,24)(16,35,37,40)(17,32,36,31)(18,33,19,21)(22,26,39,27);(1,4,5,3)(2,6,7,8)(9,12)(10,16)(11,22)(13,26)(14,28)(15,31)(17,19)(18,36)(20,37)(21,35)(23,29)(24,38)(25,39)(27,30)(32,34)(33,40);(9,12)(10,17)(11,23)(13,27)(14,28)(15,32)(16,19)(18,37)(20,36)(21,35)(22,29)(24,39)(25,38)(26,30)(31,34)(33,40)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 19392);