Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #3219×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
816 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 19072 |
A minimal faithful permutation representation — 4 generators on 197 points:
(2,7)(3,10)(4,5)(9,12)(11,13)(14,16)(17,18)(19,27)(20,24)(21,33)(22,25)(23,30)(26,36)(28,44)(29,41)(31,42)(32,39)(34,38)(35,40)(37,46)(43,45)(47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197);(1,2)(3,8)(4,12)(5,7)(6,9)(10,16)(11,15)(13,14)(17,19,22,29)(18,23,25,38)(20,28,32,45)(21,34,36,30)(24,37,39,48)(26,41,33,27)(31,47,35,46)(40,43,42,44);(1,3,6,11)(2,8,9,15)(4,10,5,13)(7,14,12,16)(17,20,22,32)(18,24,25,39)(19,28,29,45)(21,35,36,31)(23,37,38,48)(26,42,33,40)(27,43,41,44)(30,47,34,46);(2,9)(7,12)(8,15)(14,16)(18,25)(19,29)(24,39)(26,33)(28,45)(30,34)(40,42)(46,47)4619 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 12080);