Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C23×C4 |
| direct product | C137×#28633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | #3153×C137 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
772 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)(3,7)(4,5)(6,8)(9,10)(11,20)(12,25)(13,18)(14,29)(15,19)(16,22)(17,28)(21,33)(23,32)(24,37)(26,36)(27,35)(30,34)(31,39)(38,40)(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);(2,5)(6,7)(9,11,15,24,13,22,14,23)(10,16,19,32,18,20,29,37)(12,26,28,38,27,39,30,21)(17,33,35,36,34,40,25,31);(9,12,14,28,13,27,15,30)(10,17,19,25,18,34,29,35)(11,21,23,26,22,38,24,39)(16,31,32,40,20,36,37,33);(1,3,4,8)(2,6,5,7)(10,18)(16,20)(17,34)(19,29)(25,35)(31,36)(32,37)(33,40)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 21621);