Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C149 · Schur multiplier (H2) = C2×C4 |
| direct product | C149×#11855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C149 | C2×#102 |
| commutator | C2×C8 | C22×C4×C149 |
| Frattini, cosocle | C22×C8 | C23×C149 |
| prime radical | #466×C149 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ C2×C4×C8×C149 ◁ G | |
324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 9536 |
A minimal faithful permutation representation — 3 generators on 197 points:
(1,2)(3,9,11,6)(4,7)(5,8)(10,15,12,14)(13,16)(17,18)(19,29)(20,26)(21,36)(22,39)(23,28)(24,31)(25,34)(27,38)(30,42)(32,48)(33,44)(35,45)(37,46)(40,41)(43,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197);(1,3)(2,6)(4,12)(5,11)(7,15)(8,9)(10,13)(14,16)(17,19)(18,24)(20,31)(21,37)(22,40)(23,33)(25,44)(26,41)(27,46)(28,43)(29,36)(30,34)(32,38)(35,47)(39,42)(45,48);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,20,22,34,23,35,38,21)(18,25,27,26,28,36,39,45)(19,30,32,31,33,37,40,47)(24,41,42,44,43,48,46,29)7748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 4843);