Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×#7459 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C137 | D8 |
| commutator | C8 | C2×C16×C137 |
| Frattini, cosocle | C4×C16 | C22×C137 |
| socle | C2×C137 | #1370 |
| prime radical | C22×C137 | #364 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C137 ◁ C2×C16×C137 ◁ C4×C16×C137 ◁ G | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 2 generators on 169 points:
(1,2,5,9,4,12,17,26,7,11,22,25,19,28,18,31,8,13,23,27,20,29,16,32,6,24,21,30,15,10,3,14)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,3,15,21,6,16,20,23,8,18,19,22,7,17,4,5)(2,9,12,26,11,25,28,31,13,27,29,32,24,30,10,14)12056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 447);