Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#61552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C73×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #529×C73 ◁ G | |
1756 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 113 points:
(2,5)(6,8)(9,10,15,19)(11,16,23,33)(12,25,28,36)(13,20,14,18)(17,29,35,27)(21,37,26,40)(22,32,24,31)(30,39,34,38)(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)(10,16)(12,26)(13,22)(14,24)(15,23)(17,34)(18,31)(19,33)(20,32)(21,28)(25,40)(27,39)(29,38)(30,35)(36,37);(9,12)(10,17)(11,21)(13,27)(14,29)(15,28)(16,30)(18,25)(19,35)(20,36)(22,38)(23,26)(24,39)(31,37)(32,40)(33,34);(2,5)(6,8)(9,13,15,14)(10,18,19,20)(11,22,23,24)(12,27,28,29)(16,31,33,32)(17,25,35,36)(21,38,26,39)(30,37,34,40);(1,3,4,7)(2,6,5,8)(10,19)(11,23)(17,35)(18,20)(21,26)(22,24)(25,36)(38,39)4015 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54540);