Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#18156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
982 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)(4,17)(5,13)(9,25)(10,27)(11,24)(12,19)(14,31)(20,30)(22,23)(26,28)(29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,2)(3,9)(4,10)(5,19)(6,12)(7,11)(8,13)(14,28)(15,26)(16,23)(17,22)(18,27)(20,32)(21,29)(24,30)(25,31);(1,3,6,15)(2,9,12,26)(4,13,17,5)(7,16,21,18)(8,22,19,10)(11,23,29,27)(14,30,31,20)(24,25,32,28);(1,4,7,14)(2,10,11,28)(3,13,16,30)(5,18,20,15)(6,17,21,31)(8,23,24,9)(12,22,29,25)(19,27,32,26)5069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 11144);