Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19097 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #3567×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 19072 |
A minimal faithful permutation representation — 4 generators on 197 points:
(3,10)(4,5)(7,14)(8,12)(11,13)(15,16)(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);(1,2)(3,7)(4,8)(5,12)(6,9)(10,15)(11,16)(13,14)(17,19,23,31)(18,24,28,39)(20,30,35,44)(21,36,22,32)(25,38,40,48)(26,41,27,29)(33,47,42,43)(34,46,37,45);(1,3)(2,7)(4,10)(5,13)(6,11)(8,15)(9,16)(12,14)(17,20)(18,25)(19,30)(21,34)(22,37)(23,35)(24,38)(26,33)(27,42)(28,40)(29,43)(31,44)(32,45)(36,46)(39,48)(41,47);(1,4,6,5)(2,8,9,12)(3,10,11,13)(7,15,16,14)(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, 12085);