Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#19091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #3561×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 9536 |
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)(19,29,32,39)(20,33,35,41)(21,26,22,27)(24,36,40,31)(25,37,42,34)(30,38,46,48)(43,44,47,45)(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)(17,19,23,32)(18,24,28,40)(20,30,35,46)(21,36,22,31)(25,38,42,48)(26,29,27,39)(33,47,41,43)(34,45,37,44);(1,3)(2,6)(4,14)(5,10)(7,15)(8,16)(9,12)(11,13)(17,20)(18,25)(19,30)(21,34)(22,37)(23,35)(24,38)(26,41)(27,33)(28,42)(29,43)(31,44)(32,46)(36,45)(39,47)(40,48);(2,7)(6,15)(8,12)(9,16)(17,21,23,22)(18,26,28,27)(19,31,32,36)(20,34,35,37)(24,39,40,29)(25,41,42,33)(30,44,46,45)(38,47,48,43)4619 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 12079);