Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#18422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C149 |
| prime radical | #3188×C149 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 4768 |
A minimal faithful permutation representation — 4 generators on 181 points:
(1,2)(3,13)(4,7)(5,11)(6,20)(8,12)(9,15)(10,22)(14,23)(16,26)(17,29)(18,31)(19,24)(21,25)(27,32)(28,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181);(1,3)(2,9)(4,14)(5,15)(6,23)(7,17)(8,18)(10,26)(11,29)(12,28)(13,20)(16,25)(19,31)(21,27)(22,30)(24,32);(1,4,7,2)(3,14,17,9)(5,10,6,19)(8,21,25,12)(11,24,20,22)(13,30,29,32)(15,26,23,31)(16,28,18,27);(1,5,7,6)(2,10,4,19)(3,15,17,23)(8,22,25,24)(9,26,14,31)(11,21,20,12)(13,28,29,27)(16,32,18,30)5513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 11410);