Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#472×C73 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 3 generators on 105 points:
(2,8)(3,12)(4,6)(5,19)(9,25)(10,20)(11,17)(13,28)(14,21)(15,30)(16,29)(18,22)(23,27)(26,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2)(3,13)(4,17)(5,20)(6,8)(7,11)(9,15)(10,22)(12,27)(14,26)(16,23)(18,24)(19,32)(21,28)(25,29)(30,31);(1,3)(2,9,11,13)(4,16)(5,21)(6,14)(7,15)(8,23,17,26)(10,28,20,25)(12,19)(18,30)(22,29)(24,27,32,31)2482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6392);