Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#24985 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2420 |
| prime radical | C73×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,15)(4,19)(5,9)(6,13)(7,12)(8,14)(10,22)(11,18)(16,31)(17,26)(20,28)(21,27)(23,29)(24,30)(25,32)(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);(1,3,7,17,8,18,6,5)(2,9,13,11,14,26,12,15)(4,20,22,16,24,21,23,32)(10,27,19,31,29,28,30,25);(1,4)(2,10)(3,16)(5,21)(6,22)(7,23)(8,24)(9,25)(11,28)(12,19)(13,30)(14,29)(15,27)(17,20)(18,32)(26,31);(1,5,6,18,8,17,7,3)(2,11,12,9,14,15,13,26)(4,21,22,32,24,20,23,16)(10,28,19,25,29,27,30,31)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17973);