Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C22×C4 |
| direct product | C151×#13244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #466 |
| commutator | C2×C8 | C22×C4×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| prime radical | C23×C151 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 219 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 3 generators on 219 points:
(2,4)(5,6,11,18,13,19,12,37)(7,20,24,40,25,48,36,51)(8,26,29,58,31,59,30,45)(9,17,10,35,34,49,33,16)(14,38,41,22,43,23,42,32)(15,44,46,61,47,27,57,28)(21,39,54,64,55,66,62,65)(50,60,56,63,67,52,68,53)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219);(1,2,3,4)(5,7,9,32,12,24,33,38,13,25,34,22,11,36,10,23)(6,14,35,20,18,42,49,51,19,43,16,48,37,41,17,40)(8,21,27,60,30,54,61,63,31,55,44,52,29,62,28,53)(15,39,58,50,46,65,59,68,47,66,45,67,57,64,26,56);(5,8,9,27,12,30,33,61,13,31,34,44,11,29,10,28)(6,15,35,58,18,46,49,59,19,47,16,45,37,57,17,26)(7,21,32,60,24,54,38,63,25,55,22,52,36,62,23,53)(14,39,20,50,42,65,51,68,43,66,48,67,41,64,40,56)7852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6232);