Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#12915 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C151 | #120 |
| commutator | C23 | C22×C8×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C2×C151 | #1850 |
| prime radical | C2×#41×C151 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C151 ◁ C22×C8×C151 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 215 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 215 points:
(1,2,5,10,6,11,20,30,7,12,21,31,22,32,43,53)(3,8,15,25,16,26,39,49,14,24,37,47,38,48,58,62)(4,9,18,28,19,29,42,52,17,27,40,50,41,51,59,63)(13,33,35,54,36,55,57,64,34,23,44,45,56,46,60,61)(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);(1,3,5,15,6,16,20,39,7,14,21,37,22,38,43,58)(2,8,10,25,11,26,30,49,12,24,31,47,32,48,53,62)(4,13,18,35,19,36,42,57,17,34,40,44,41,56,59,60)(9,23,28,45,29,46,52,61,27,33,50,54,51,55,63,64);(1,4)(2,9)(3,13)(5,18)(6,19)(7,17)(8,23)(10,28)(11,29)(12,27)(14,34)(15,35)(16,36)(20,42)(21,40)(22,41)(24,33)(25,45)(26,46)(30,52)(31,50)(32,51)(37,44)(38,56)(39,57)(43,59)(47,54)(48,55)(49,61)(53,63)(58,60)(62,64)9664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5903);