Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19036 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #3559×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 19072 |
A minimal faithful permutation representation — 4 generators on 181 points:
(1,2)(3,11)(4,8)(5,9)(6,10)(7,12)(13,15)(14,16)(17,18,22,25)(19,26,29,32)(20,24,21,30)(23,27,31,28)(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)(2,7)(4,14)(5,12)(6,13)(8,11)(9,15)(10,16)(17,19,22,29)(18,23,25,31)(20,28,21,27)(24,32,30,26);(1,3)(2,7)(4,12)(5,14)(6,13)(8,15)(9,11)(10,16)(17,18)(19,23)(20,24)(21,30)(22,25)(26,27)(28,32)(29,31);(1,4,6,5)(2,8,10,9)(3,12,13,14)(7,15,16,11)(17,20,22,21)(18,24,25,30)(19,27,29,28)(23,26,31,32)5513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 12024);