Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C149 · Schur multiplier (H2) = C22×C4 |
| direct product | C149×#9346 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | #386 |
| commutator | C22×C4 | C22×C4×C149 |
| Frattini, cosocle | C23×C4 | C23×C149 |
| prime radical | C24×C149 | #41 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 9536 |
A minimal faithful permutation representation — 3 generators on 181 points:
(2,6)(3,9)(4,12)(8,14)(10,11)(13,15)(17,18)(19,22,26,29)(20,23)(21,24)(25,28,31,32)(27,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181);(1,2,4,6,5,8,12,14)(3,7,10,13,11,16,9,15)(17,19)(18,22,24,29)(20,25)(21,26)(23,28,30,32)(27,31);(1,3,5,11)(2,7,8,16)(4,10,12,9)(6,13,14,15)(17,20,21,27)(18,23,24,30)(19,25,26,31)(22,28,29,32)5960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 2334);