Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#18216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
988 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(2,8)(3,14)(4,16)(5,19)(9,27)(10,23)(11,25)(12,20)(13,26)(17,24)(21,32)(28,29)(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)(3,9)(4,17)(5,20)(6,12)(7,13)(8,19)(10,16)(11,22)(14,29)(15,27)(18,24)(21,25)(23,31)(26,32)(28,30);(1,3,7,4)(2,9,13,17)(5,18,21,15)(6,14,22,16)(8,23,26,28)(10,12,29,11)(19,31,32,30)(20,24,25,27);(1,4,7,3)(2,10,13,29)(5,18,21,15)(6,16,22,14)(8,24,26,27)(9,12,17,11)(19,31,32,30)(20,23,25,28)3139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 11204);