Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#19901 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | #3294×C137 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C42×C137 ◁ G | |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2,5,8)(3,9,10,16)(4,13,14,7)(6,11,15,12)(17,18)(19,22)(20,23)(21,25)(24,28)(26,29)(27,31)(30,32)(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);(1,3,5,10)(2,6,8,15)(4,11,14,12)(7,16,13,9)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(3,10)(6,15)(9,16)(11,12)(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(3,11)(4,14)(6,16)(7,13)(9,15)(10,12)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 12889);