Finite Group DatabasebetaFinite Group Databasebeta| order | 14641 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C112 · Schur multiplier (H2) = C112 |
| unambiguous semidirect product | H(3,𝔽11)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C11 | H(3,𝔽11) |
| commutator, Frattini, cosocle | C112 | C112 |
| LCS | G ▷ C112 ▷ C11 ▷ C1 | |
| UCS | C1 ◁ C11 ◁ C112 ◁ G | |
| LECS | G ▷ C112 ▷ C11 ▷ C1 | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 121 |
A minimal faithful permutation representation — 2 generators on 121 points:
(1,2,4,8,16,31,47,62,75,87,99)(3,5,11,19,34,50,65,78,89,100,112)(6,13,27,32,51,63,79,93,106,117,111)(7,12,25,39,53,69,81,92,103,101,113)(9,20,40,57,72,84,88,102,114,15,26)(10,23,43,58,73,85,97,110,121,98,14)(17,35,49,68,76,90,104,115,61,60,21)(18,37,55,71,83,96,109,120,86,29,28)(22,41,56,48,66,77,91,105,116,30,44)(24,36,33,52,70,82,95,108,119,74,45)(38,54,67,64,80,94,107,118,46,59,42);(2,5,12,26,44,59,60,45,29,14,6)(4,9,21,10,11,22,24,13,25,42,28)(8,17,19,36,39,18,20,23,41,27,38)(16,32,43,37,33,35,54,56,40,53,34)(31,48,55,50,67,58,69,49,51,57,52)(47,63,73,71,70,68,64,66,72,81,65)(62,76,78,82,92,83,84,85,77,79,80)(75,88,90,97,89,91,95,93,103,94,96)(87,100,101,102,105,107,104,108,109,110,106)Polycyclic presentation:
11^4|b^a=bc,c^a=cd241 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14641, 7);