Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#26852 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C2×#41×C137 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2)(3,8)(4,6)(5,7)(9,10)(11,22)(12,28)(13,32)(14,20)(15,21)(16,25)(17,30)(18,23)(19,33)(24,36)(26,35)(27,37)(29,38)(31,39)(34,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(1,3,5,4)(2,6,7,8)(9,11,14,25,15,27,33,26)(10,16,19,22,21,35,20,37)(12,29,30,40,31,13,24,23)(17,32,28,34,36,38,39,18);(1,4,5,3)(2,6,7,8)(9,12,14,30,15,31,33,24)(10,17,19,28,21,36,20,39)(11,23,25,29,27,40,26,13)(16,34,22,38,35,18,37,32);(2,7)(6,8)(9,13,14,23,15,29,33,40)(10,18,19,32,21,34,20,38)(11,24,25,12,27,30,26,31)(16,17,22,28,35,36,37,39)5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 19840);