Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#25271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | #525×C137 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2)(3,6)(4,5)(7,8)(9,10,15,28,14,19,13,18)(11,16,29,40,22,32,21,31)(12,23,25,17,27,34,26,35)(20,36,37,30,24,39,38,33)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(2,5)(6,8)(9,11,13,21,14,22,15,29)(10,16,18,31,19,32,28,40)(12,24,26,37,27,20,25,38)(17,33,23,39,35,30,34,36);(1,3,4,7)(2,6,5,8)(9,12,14,27)(10,17,19,35)(11,20,22,24)(13,25,15,26)(16,30,32,33)(18,34,28,23)(21,37,29,38)(31,39,40,36);(2,5)(6,8)(9,13,14,15)(10,18,19,28)(11,21,22,29)(12,25,27,26)(16,31,32,40)(17,34,35,23)(20,37,24,38)(30,39,33,36)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 18259);