Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C22×C4 |
| direct product | C137×#26725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C137 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C24×C137 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C137 ◁ C4×C22⋊C4×C137 ◁ G | |
748 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)(3,6)(4,5)(7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,22)(20,23)(21,24)(25,32)(26,30)(27,29)(28,31)(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);(2,5)(6,8)(17,19,20,26)(18,22,23,30)(21,25,28,27)(24,32,31,29);(1,3,4,7)(2,6,5,8)(10,13)(14,16)(18,23)(19,25)(21,28)(22,29)(26,27)(30,32);(2,5)(6,8)(9,11,12,15)(10,14,13,16)7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 19713);