Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C27 |
| direct product | C131×#23425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C22×#41×C131 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G | |
1938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2)(3,4)(9,10,15,20)(11,21,23,32)(12,26,29,33)(13,19,14,18)(16,25,31,24)(17,27,34,28)(22,36,37,30)(35,38,40,39)(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);(2,4)(5,6)(7,8)(9,11)(10,16)(12,22)(13,25)(14,24)(15,23)(17,30)(18,32)(19,21)(20,31)(26,40)(27,39)(28,38)(29,37)(33,35)(34,36);(6,8)(9,12,15,29)(10,17,20,34)(11,22,23,37)(13,28,14,27)(16,30,31,36)(18,26,19,33)(21,35,32,40)(24,39,25,38);(11,23)(16,31)(21,32)(22,37)(24,25)(30,36)(35,40)(38,39)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 16413);