Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#18138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C149 |
| prime radical | C25×C149 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G | |
1054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 4768 |
A minimal faithful permutation representation — 4 generators on 181 points:
(1,2,6,10)(3,11,13,27)(4,15,17,29)(5,8,19,23)(7,20,22,12)(9,24,26,18)(14,25,28,32)(16,21,30,31)(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);(1,3,5,14)(2,7,8,21)(4,16,18,12)(6,13,19,28)(9,25,15,11)(10,22,23,31)(17,30,24,20)(26,32,29,27);(4,17)(9,26)(11,27)(12,20)(15,29)(16,30)(18,24)(25,32);(2,8)(7,21)(9,15)(10,23)(11,25)(22,31)(26,29)(27,32)5513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 11126);