Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#18994 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C149 |
| prime radical | #3153×C149 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 9536 |
A minimal faithful permutation representation — 4 generators on 189 points:
(2,5)(3,7)(6,8)(9,10)(11,21)(12,25)(13,20)(14,19)(15,18)(16,23)(17,26)(22,30)(24,33)(27,34)(28,31)(29,32)(35,37)(36,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189);(3,7)(5,8)(9,11)(10,16)(12,22)(13,28)(14,23)(15,24)(17,30)(18,31)(19,33)(20,21)(25,39)(26,37)(27,38)(29,36)(32,40)(34,35);(1,2)(3,8)(4,6)(5,7)(9,12,15,27)(10,17,18,32)(11,22,24,38)(13,26,14,29)(16,30,31,40)(19,25,20,34)(21,35,33,39)(23,36,28,37);(10,18)(16,31)(17,32)(19,20)(21,33)(25,34)(30,40)(35,39)5066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 11982);