Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#24719 |
| 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 ◁ C2×#117×C137 ◁ G | |
738 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 165 points:
(5,6,8,9)(7,11,12,10)(13,14,19,27,18,23,17,22)(15,20,24,28,16,26,25,21)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165);(1,2)(3,4)(6,9)(10,11)(13,15)(14,20)(16,18)(17,25)(19,24)(21,22)(23,26)(27,28);(2,4)(13,16,18,15)(14,21,23,28)(17,25,19,24)(20,27,26,22);(5,7,8,12)(6,10,9,11)(13,17,18,19)(14,22,23,27)(15,24,16,25)(20,28,26,21)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 17707);