Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C137 · Schur multiplier (H2) = C27 |
| direct product | C137×#20918 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C137 | C22×D4 |
| commutator | C2×C4 | C23×C4×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| socle | C22×C137 | C2×C4×D4 |
| prime radical | C2×#575×C137 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C137 ◁ C22×M16×C137 ◁ G | |
1714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 157 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 4 generators on 157 points:
(2,4)(6,10,12,15)(7,13,14,16)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157);(1,2,3,4)(5,6,8,15,9,12,17,10)(7,11,16,20,14,19,13,18);(5,7)(6,11)(8,16)(9,14)(10,18)(12,19)(13,17)(15,20);(6,12)(10,15)(11,19)(18,20)8768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 13906);