Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C22 |
| direct product | C2×Q128×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C151 | D32 |
| commutator, Frattini, cosocle | C32 | C23×C151 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C4×C151 ◁ C2×C8×C151 ◁ C2×C16×C151 ◁ C2×C32×C151 ◁ G | |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 281 |
| transitive degree | μt(G) = 38656 |
A minimal faithful permutation representation — 3 generators on 281 points:
(1,2)(131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281);(3,4,10,16)(5,17,22,62)(6,23,29,59)(7,30,34,91)(8,35,38,97)(9,39,37,15)(11,41,45,18)(12,46,50,26)(13,51,54,25)(14,55,57,32)(19,65,67,126)(20,68,69,128)(21,70,40,61)(24,52,77,119)(27,83,86,124)(28,87,85,73)(31,47,94,111)(33,95,79,90)(36,60,98,125)(42,102,104,75)(43,105,106,74)(44,64,58,100)(48,112,114,129)(49,82,99,109)(53,80,89,116)(56,101,121,63)(66,127,92,113)(71,108,122,78)(72,107,123,81)(76,120,88,118)(84,117,130,103)(93,115,96,110);(3,5,10,22)(4,11,16,45)(6,24,29,77)(7,31,34,94)(8,36,38,98)(9,40,37,21)(12,47,50,111)(13,52,54,119)(14,56,57,121)(15,58,39,44)(17,59,62,23)(18,46,41,26)(19,51,67,25)(20,55,69,32)(27,84,86,130)(28,88,85,76)(30,42,91,104)(33,96,79,93)(35,43,97,106)(48,113,114,127)(49,115,99,110)(53,120,89,118)(60,124,125,83)(61,73,70,87)(63,112,101,129)(64,82,100,109)(65,122,126,71)(66,80,92,116)(68,123,128,72)(74,108,105,78)(75,107,102,81)(90,117,95,103)10570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6728);