Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C149 · Schur multiplier (H2) = C23 |
| direct product | C149×#11703 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C149 | #102 |
| commutator | C2×C8 | C22×C4×C149 |
| Frattini, cosocle | C22×C8 | C23×C149 |
| socle | C22×C149 | C2×#102 |
| prime radical | #3050×C149 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ C23×C8×C149 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 9536 |
A minimal faithful permutation representation — 3 generators on 189 points:
(1,2)(3,7,8,5)(4,6)(9,10)(11,21,24,38)(12,17)(13,27)(14,19)(15,20)(16,23,32,39)(18,26)(22,37,25,35)(28,33,40,31)(29,36)(30,34)(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);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,22)(13,28)(14,25)(15,24)(17,31)(18,35)(19,33)(20,32)(21,34)(23,29)(26,39)(27,38)(30,40)(36,37);(9,12,15,14)(10,17,20,19)(11,22,24,25)(13,26,30,29)(16,31,32,33)(18,34,36,27)(21,37,38,35)(23,28,39,40)8642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 4691);