Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#19712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3169 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,13)(11,16)(12,15)(18,22)(19,26)(20,23)(24,27)(25,30)(28,31)(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);(3,11)(7,15)(10,16)(12,13)(17,18,23,30,21,25,20,22)(19,27,31,29,28,24,26,32);(1,3,5,13,6,11,4,12)(2,7,8,10,9,15,14,16)(17,19,23,31,21,28,20,26)(18,24,30,32,25,27,22,29);(1,4,6,5)(2,8,9,14)(3,12,11,13)(7,10,15,16)(19,28)(24,27)(26,31)(29,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12700);