Finite Group DatabasebetaFinite Group Databasebeta| order | 14641 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C121 · Schur multiplier (H2) = C112 |
| unambiguous semidirect product | C112⋊C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C112 | C112 |
| commutator | C11 | C11×C121 |
| prime radical | C113 | C11 |
| LCS | G ▷ C11 ▷ C1 | |
| UCS | C1 ◁ C112 ◁ G | |
| LECS | G ▷ C112 ▷ C1 | |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 242 |
| transitive degree | μt(G) = 1331 |
A minimal faithful permutation representation — 2 generators on 242 points:
(1,2,4,8,15,26,42,60,73,86,99)(3,6,10,17,28,44,62,75,88,101,112)(5,11,21,37,56,71,84,97,110,121,111)(7,13,20,31,47,64,77,90,103,100,113)(9,18,32,52,70,83,96,109,120,98,12)(14,24,36,51,46,66,80,94,87,102,114)(16,29,48,67,81,95,108,119,85,23,22)(19,34,27,45,65,79,93,107,118,72,39)(25,40,55,54,49,68,82,74,89,104,115)(30,50,69,61,76,91,105,116,41,58,35)(33,53,43,63,78,92,106,117,59,57,38)(122,123,125,128,132,137,143,150,158,167,177,124,126,129,133,138,144,151,159,168,178,188,127,130,134,139,145,152,160,169,179,189,198,131,135,140,146,153,161,170,180,190,199,207,136,141,147,154,162,171,181,191,200,208,215,142,148,155,163,172,182,192,201,209,216,222,149,156,164,173,183,193,202,210,217,223,228,157,165,174,184,194,203,211,218,224,229,233,166,175,185,195,204,212,219,225,230,234,237,176,186,196,205,213,220,226,231,235,238,240,187,197,206,214,221,227,232,236,239,241,242);(2,5,12,23,39,57,58,40,24,13,6)(4,9,19,35,36,10,11,22,38,55,20)(8,16,30,31,21,34,54,17,18,33,51)(15,27,46,37,53,47,32,50,28,29,49)(26,43,44,45,64,48,66,52,68,56,69)(42,61,71,82,70,80,67,77,65,62,63)(60,74,81,75,76,83,90,78,84,94,79)(73,87,92,96,88,89,93,97,103,91,95)(86,100,104,106,108,110,101,102,105,107,109)(99,112,113,114,115,116,117,118,119,120,121)Polycyclic presentation:
11^4|a^11=d,b^a=bc1441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14641, 3);