Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#23997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #2404 |
| commutator, Frattini, cosocle | C24 | C24×C73 |
| prime radical | C73×#3026 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C24×C73 ◁ G | |
1210 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)(3,7)(4,8)(5,9)(6,10)(11,18)(12,19)(13,20)(14,26)(15,28)(16,22)(17,23)(21,29)(24,32)(25,31)(27,30)(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);(1,3,6,13)(2,7,10,20)(4,14)(5,12,17,25)(8,18)(9,19,23,31)(11,16)(15,27)(21,30)(22,26)(24,29)(28,32);(1,4)(2,8)(3,11)(5,15)(6,16)(7,18)(9,21)(10,22)(12,24)(13,14)(17,29)(19,30)(20,26)(23,28)(25,27)(31,32);(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,21)(10,23)(11,24)(13,25)(14,27)(16,29)(18,30)(20,31)(22,28)(26,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16985);