Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C149 · Schur multiplier (H2) = C24×C4 |
| direct product | C149×#18400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C149 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
978 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 4768 |
A minimal faithful permutation representation — 4 generators on 181 points:
(2,9)(3,14)(4,16)(5,19)(10,25)(11,27)(12,20)(13,26)(15,18)(17,30)(21,22)(23,32)(24,28)(29,31)(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)(3,10)(4,17)(5,20)(6,23)(7,12)(8,13)(9,19)(11,14)(15,30)(16,28)(18,25)(21,26)(22,32)(24,29)(27,31);(1,3,8,4)(2,10,13,17)(5,18,22,15)(6,14,7,16)(9,24,26,27)(11,12,28,23)(19,29,21,31)(20,25,32,30);(1,4,8,3)(2,11,13,28)(5,18,22,15)(6,16,7,14)(9,25,26,30)(10,12,17,23)(19,29,21,31)(20,24,32,27)6407 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 11388);