Finite Group DatabasebetaFinite Group Databasebeta| order | 14641 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C113 · Schur multiplier (H2) = C112 |
| direct product | C11×11−1+2 |
| unambiguous semidirect product | C121⋊C112 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C112 | C112 |
| commutator, Frattini, cosocle | C11 | C113 |
| prime radical | C113 | C11 |
| LCS | G ▷ C11 ▷ C1 | |
| UCS | C1 ◁ C112 ◁ G | |
| LECS | G ▷ C11 ▷ C1 | |
302 conjugacy classes of subgroups.
| minimal degree | μ(G) = 132 |
| transitive degree | μt(G) = 1331 |
A minimal faithful permutation representation — 3 generators on 132 points:
(1,2,3,4,5,6,7,8,9,10,11);(12,13,15,19,26,37,53,71,84,97,110,14,17,21,28,39,55,73,86,99,112,123,18,24,31,42,58,75,88,101,114,111,124,25,35,47,62,57,77,91,105,98,113,125,36,51,66,65,60,79,93,85,100,115,126,52,69,46,41,61,80,72,87,102,116,127,70,68,49,44,64,54,74,89,103,117,128,83,50,30,45,38,56,76,90,104,118,129,96,34,33,27,40,59,78,92,106,119,130,109,23,20,29,43,63,81,94,107,120,131,122,16,22,32,48,67,82,95,108,121,132);(13,16,23,34,50,68,69,51,35,24,17)(15,20,30,46,47,21,22,33,49,66,31)(19,27,41,42,32,45,65,28,29,44,62)(26,38,57,48,64,58,43,61,39,40,60)(37,54,55,56,75,59,77,63,79,67,80)(53,72,82,93,81,91,78,88,76,73,74)(71,85,92,86,87,94,101,89,95,105,90)(84,98,103,107,99,100,104,108,114,102,106)(97,111,115,117,119,121,112,113,116,118,120)(110,123,124,125,126,127,128,129,130,131,132)1441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14641, 13);