Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#18696 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2)(3,8)(4,9)(5,14)(6,10)(7,11)(12,15)(13,16)(17,18)(19,27)(20,25)(21,24)(22,26)(23,29)(28,32)(30,31)(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)(2,7)(4,11)(5,13)(6,12)(8,14)(9,15)(10,16)(17,19,22,30)(18,23,26,32)(20,28,21,29)(24,31,25,27);(1,3)(2,8)(4,13)(5,11)(6,12)(7,14)(9,16)(10,15)(18,24)(20,21)(23,31)(25,26)(27,32)(28,29);(1,4,6,5)(2,9,10,14)(3,11,12,13)(7,15,16,8)(17,20,22,21)(18,25,26,24)(19,28,30,29)(23,27,32,31)5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 11684);