Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33854 |
| 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 | |
656 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)(4,16)(5,6)(9,26)(10,28)(11,30)(12,25)(14,31)(15,21)(17,22)(19,20)(23,27)(24,29)(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)(3,9)(4,17)(5,11)(6,22)(7,12)(8,16)(10,14)(13,27)(15,28)(18,23)(19,25)(20,30)(21,24)(26,31)(29,32);(1,3)(2,9)(4,14)(5,21)(6,13)(7,15)(8,23)(10,17)(11,24)(12,28)(16,18)(19,32)(20,31)(22,27)(25,29)(26,30);(1,3)(2,10)(4,18)(5,13)(6,21)(7,15)(8,24)(9,17)(11,23)(12,26)(14,16)(19,31)(20,32)(22,29)(25,27)(28,30)5069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26842);