Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C137 · Schur multiplier (H2) = C26 |
| direct product | C137×#20839 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C137 | C24 |
| commutator | C23 | C23×C4×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| socle | C23×C137 | C23×C4 |
| prime radical | C22×#41×C137 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C137 ◁ G | |
1458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 161 points:
(1,2)(3,4)(5,6)(7,8)(9,10,14,17,13,16,22,23)(11,18,20,24,19,12,15,21)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161);(2,4)(9,11,14,20,13,19,22,15)(10,12,17,21,16,18,23,24);(6,8)(9,12)(10,15)(11,17)(13,18)(14,21)(16,20)(19,23)(22,24);(10,16)(12,18)(17,23)(21,24)10412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 13827);