Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C137 · Schur multiplier (H2) = C27 |
| direct product | C137×#36691 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C137 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C137 |
| socle | C23×C137 | C25 |
| prime radical | C24×C137 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C137 ◁ G | |
1474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 5 generators on 169 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,28)(26,30)(27,29)(31,32)(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);(9,11,12,16)(10,13,14,15)(18,22)(23,28)(24,29)(30,32);(1,3,4,8)(2,5,6,7)(9,10)(11,15)(12,14)(13,16)(17,19)(18,23)(20,26)(21,25)(22,28)(24,30)(27,31)(29,32);(10,14)(13,15)(19,25)(23,28)(26,31)(30,32);(17,20,21,27)(18,24,22,29)(19,26,25,31)(23,30,28,32)7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 29679);