Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C151 · Schur multiplier (H2) = C22×C4 |
| direct product | C151×#23368 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C151 | C24 |
| commutator | C23 | C23×C4×C151 |
| Frattini, cosocle | C22×C4 | C24×C151 |
| socle, prime radical | C23×C151 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C151 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 38656 |
A minimal faithful permutation representation — 4 generators on 191 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,18)(12,16)(13,22)(14,17)(15,21)(19,24)(20,23)(25,26,29,32,28,31,36,39)(27,33,35,40,34,30,37,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191);(3,8)(5,7)(9,11,14,21)(10,15,17,18)(12,20,13,19)(16,24,22,23);(1,3,4,8)(2,5,6,7)(9,12,14,13)(10,16,17,22)(11,19,21,20)(15,23,18,24)(25,27,28,34)(26,30,31,33)(29,35,36,37)(32,38,39,40);(2,6)(5,7)(9,13,14,12)(10,16,17,22)(11,20,21,19)(15,23,18,24)(27,34)(30,33)(35,37)(38,40)7852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16356);