Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#60586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C73×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×#117×C73 ◁ G | |
2024 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)(3,6)(4,5)(7,8)(9,10)(11,16)(12,18)(13,19)(14,28)(15,20)(17,25)(21,30)(22,31)(23,38)(24,32)(26,33)(27,34)(29,35)(36,39)(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)(6,8)(9,11,15,24)(10,16,20,32)(12,21,26,36)(13,22,14,23)(17,29,34,40)(18,30,33,39)(19,31,28,38)(25,35,27,37);(9,12)(10,17)(11,21)(13,25)(14,27)(15,26)(16,29)(18,28)(19,33)(20,34)(22,35)(23,37)(24,36)(30,38)(31,39)(32,40);(1,3,4,7)(2,6,5,8)(9,12)(10,18)(11,21)(13,27)(14,25)(15,26)(16,30)(17,28)(19,34)(20,33)(22,37)(23,35)(24,36)(29,38)(31,40)(32,39);(9,13,15,14)(10,19,20,28)(11,22,24,23)(12,25,26,27)(16,31,32,38)(17,33,34,18)(21,35,36,37)(29,39,40,30)4453 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53574);