Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C2×C4×C137 ◁ #443×C137 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 4 generators on 169 points:
(2,8)(3,13)(4,17)(5,6)(9,10)(11,27)(12,26)(14,31)(15,29)(16,22)(18,23)(20,21)(24,25)(28,30)(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);(1,2,7,12)(3,14,16,9)(4,18,21,27)(5,11,6,23)(8,20,26,17)(10,29,31,15)(13,28,22,25)(19,30,32,24);(1,3)(2,9)(4,15)(5,22)(6,13)(7,16)(8,24)(10,27)(11,28)(12,14)(17,19)(18,31)(20,32)(21,29)(23,25)(26,30);(1,3)(2,10)(4,19)(5,13)(6,22)(7,16)(8,25)(9,27)(11,30)(12,31)(14,18)(15,17)(20,29)(21,32)(23,24)(26,28)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26846);