Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#12742 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #1786 |
| commutator | C2×C8 | C22×C4×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| prime radical | C2×#578×C151 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 215 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 215 points:
(1,2)(3,13)(4,18,20,9)(5,22)(6,27)(7,11)(8,15)(10,25)(12,24)(14,40,42,38)(16,46)(17,39)(19,50,53,56)(21,33,52,49)(23,36)(26,37)(28,34)(29,41,47,63)(30,45)(31,57)(32,54,48,62)(35,44)(43,59,55,61)(51,58,64,60)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215);(1,3,7,17)(2,8,11,30)(4,14,20,42)(5,23,26,57)(6,28,24,16)(9,29,18,47)(10,34,35,46)(12,36,27,31)(13,37,39,22)(15,44,45,25)(19,51,53,64)(21,55,52,43)(32,59,48,61)(33,60,49,58)(38,50,40,56)(41,62,63,54);(1,4)(2,9)(3,14)(5,19)(6,21)(7,20)(8,29)(10,32)(11,18)(12,33)(13,38)(15,41)(16,43)(17,42)(22,56)(23,51)(24,52)(25,54)(26,53)(27,49)(28,55)(30,47)(31,58)(34,59)(35,48)(36,60)(37,50)(39,40)(44,62)(45,63)(46,61)(57,64)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5730);