Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#25314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C23×C137 | C2×#41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2)(3,7)(4,5)(6,8)(9,10,13,17,14,18,27,34)(11,15,20,29,21,30,38,40)(12,22,24,32,25,33,26,16)(19,35,36,31,23,39,37,28)(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);(2,5)(6,7)(9,11,13,20,14,21,27,38)(10,15,17,29,18,30,34,40)(12,23,24,37,25,19,26,36)(16,31,22,39,32,28,33,35);(9,12,14,25)(10,16,18,32)(11,19,21,23)(13,26,27,24)(15,28,30,31)(17,33,34,22)(20,37,38,36)(29,39,40,35);(1,3,4,8)(2,6,5,7)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 18302);