Finite Group DatabasebetaFinite Group Databasebeta| order | 14641 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C121 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C121⋊C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, cosocle | C112 | C112 |
| commutator | C11 | C11×C121 |
| LCS | G ▷ C11 ▷ C1 | |
| UCS | C1 ◁ C112 ◁ G | |
| LECS | G ▷ C112 ▷ C1 | |
49 conjugacy classes of subgroups.
| minimal degree | μ(G) = 242 |
| transitive degree | μt(G) = 14641 |
A minimal faithful permutation representation — 2 generators on 242 points:
(2,4,7,12,20,32,49,68,82,96,110)(5,9,15,24,37,55,8,13,21,33,50)(10,17,27,41,14,22,34,51,16,25,38)(18,29,44,23,35,52,26,39,56,28,42)(30,46,63,45,61,43,59,40,57,36,53)(47,65,54,69,58,71,60,73,62,75,64)(66,79,74,87,78,72,85,77,70,83,76)(80,93,90,86,99,92,89,84,97,91,88)(94,107,105,103,101,98,111,106,104,102,100)(108,121,120,119,118,117,116,115,114,113,112)(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);(1,2,5,10,18,30,47,66,80,94,108,3,4,8,14,23,36,54,70,84,98,112,6,7,9,16,26,40,58,72,86,100,113,11,12,13,17,28,43,60,74,88,101,114,19,20,15,22,29,45,62,76,89,102,115,31,32,21,25,35,46,64,77,90,103,116,48,49,24,27,39,53,65,78,91,104,117,67,68,33,34,42,57,69,79,92,105,118,81,82,37,38,44,59,71,83,93,106,119,95,96,50,41,52,61,73,85,97,107,120,109,110,55,51,56,63,75,87,99,111,121)Polycyclic presentation:
11^4|a^11=d,b^11=c,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, 4);