Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C25 |
| direct product | C149×#18425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C149 |
| prime radical | #3536×C149 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 4768 |
A minimal faithful permutation representation — 4 generators on 181 points:
(1,2,7,4)(3,13,17,27)(5,11,6,19)(8,12,24,20)(9,22,14,15)(10,23,18,21)(16,29,31,25)(26,32,30,28)(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);(1,3,7,17)(2,9,4,14)(5,15,6,22)(8,16,24,31)(10,25,18,29)(11,27,19,13)(12,26,20,30)(21,28,23,32);(1,4,7,2)(3,14,17,9)(5,10,6,18)(8,20,24,12)(11,23,19,21)(13,28,27,32)(15,25,22,29)(16,30,31,26);(1,5,7,6)(2,10,4,18)(3,15,17,22)(8,21,24,23)(9,25,14,29)(11,20,19,12)(13,26,27,30)(16,28,31,32)5513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 11413);