Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19089 |
| 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 | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 19072 |
A minimal faithful permutation representation — 4 generators on 197 points:
(1,2)(3,9)(4,12)(5,7)(6,11)(8,13)(10,16)(14,15)(17,18,23,28)(19,29,31,41)(20,33,35,42)(21,27,22,26)(24,36,39,32)(25,37,40,34)(30,38,44,48)(43,45,47,46)(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);(4,13)(8,12)(9,16)(11,14)(17,19)(18,24)(20,30)(21,36)(22,32)(23,31)(25,38)(26,41)(27,29)(28,39)(33,47)(34,46)(35,44)(37,45)(40,48)(42,43);(1,3)(2,6)(4,14)(5,10)(7,15)(8,16)(9,12)(11,13)(17,20,23,35)(18,25,28,40)(19,30,31,44)(21,34,22,37)(24,38,39,48)(26,33,27,42)(29,43,41,47)(32,45,36,46);(2,7)(6,15)(8,12)(9,16)(19,31)(24,39)(29,41)(30,44)(32,36)(38,48)(43,47)(45,46)4619 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 12077);