Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#19095 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C73 |
| prime radical | C73×#3568 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 121 points:
(3,10)(4,5)(7,14)(8,12)(11,13)(15,16)(17,18,23,28)(19,29,31,41)(20,33,35,42)(21,27,22,26)(24,36,39,32)(25,37,40,34)(30,38,44,48)(43,45,47,46)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(1,2)(3,7)(4,8)(5,12)(6,9)(10,15)(11,16)(13,14)(17,19)(18,24)(20,30)(21,36)(22,32)(23,31)(25,38)(26,41)(27,29)(28,39)(33,47)(34,46)(35,44)(37,45)(40,48)(42,43);(1,3)(2,7)(4,10)(5,13)(6,11)(8,15)(9,16)(12,14)(17,20)(18,25)(19,30)(21,34)(22,37)(23,35)(24,38)(26,33)(27,42)(28,40)(29,43)(31,44)(32,45)(36,46)(39,48)(41,47);(1,4,6,5)(2,8,9,12)(3,10,11,13)(7,15,16,14)(19,31)(24,39)(29,41)(30,44)(32,36)(38,48)(43,47)(45,46)2263 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 12083);