Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19081 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #532×C149 | C22 |
| 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:
(2,7)(3,11)(4,5)(9,10)(12,13)(14,15)(17,18,23,20)(19,27,30,32)(21,26,22,25)(24,31,28,29)(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);(1,2)(3,8)(4,9)(5,7)(6,10)(11,15)(12,14)(13,16)(17,19)(18,24)(20,28)(21,29)(22,31)(23,30)(25,27)(26,32);(1,3,6,13)(2,8,10,16)(4,11,5,12)(7,14,9,15)(17,20,23,18)(19,28,30,24)(21,25,22,26)(27,31,32,29);(1,4,6,5)(2,9,10,7)(3,12,13,11)(8,14,16,15)(17,21,23,22)(18,25,20,26)(19,29,30,31)(24,27,28,32)5960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 12069);