Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#18414 |
| 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 ◁ C23×C4×C137 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 4 generators on 169 points:
(2,7)(3,11)(4,14)(8,20)(9,18)(10,15)(12,24)(13,27)(16,29)(19,22)(21,31)(23,30)(25,26)(28,32)(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)(3,8)(4,15)(5,10)(6,9)(7,14)(11,22)(12,21)(13,28)(16,30)(17,23)(18,29)(19,26)(20,27)(24,32)(25,31);(3,12)(4,16)(7,18)(8,21)(11,24)(13,27)(14,29)(15,30)(19,31)(20,28)(22,32)(25,26);(1,3)(2,8)(4,13)(5,12)(6,11)(7,19)(9,22)(10,21)(14,26)(15,28)(16,25)(17,24)(18,20)(23,32)(27,29)(30,31)5069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 11402);