Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#9280 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #386 |
| commutator | C42 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C23×C73 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 121 points:
(2,6,8,11)(3,9,10,12)(17,18)(19,27)(20,31,33,24)(21,34)(22,26)(23,29)(25,36)(28,41,44,48)(30,42)(32,39,35,40)(37,43,47,45)(38,46)(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);(1,2,4,11,5,8,13,6)(3,7,12,15,10,16,9,14)(17,19,21,29,22,30,36,46)(18,23,25,27,26,38,34,42)(20,28,35,45,33,44,32,43)(24,37,40,41,31,47,39,48);(1,3)(2,7)(4,12)(5,10)(6,14)(8,16)(9,13)(11,15)(17,20,22,33)(18,24,26,31)(19,28,30,44)(21,35,36,32)(23,37,38,47)(25,40,34,39)(27,41,42,48)(29,45,46,43)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2268);