Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#61207 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C73×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #532×C73 ◁ G | |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 113 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,18)(13,19)(14,28)(15,20)(17,24)(21,30)(22,31)(23,33)(25,34)(26,32)(27,35)(29,37)(36,39)(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)(2,5)(4,8)(6,7)(9,11,15,23)(10,16,20,33)(12,21,25,38)(13,26,14,22)(17,29,35,39)(18,30,34,40)(19,32,28,31)(24,37,27,36);(9,12)(10,17)(11,21)(13,24)(14,27)(15,25)(16,29)(18,28)(19,34)(20,35)(22,36)(23,38)(26,37)(30,31)(32,40)(33,39);(3,8)(5,7)(9,12)(10,18)(11,21)(13,27)(14,24)(15,25)(16,30)(17,28)(19,35)(20,34)(22,37)(23,38)(26,36)(29,31)(32,39)(33,40);(9,13,15,14)(10,19,20,28)(11,22,23,26)(12,24,25,27)(16,31,33,32)(17,34,35,18)(21,36,38,37)(29,30,39,40)4015 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54195);