Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#26719 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C22×D4×C131 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C4×C4⋊C4×C131 ◁ G | |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,14)(12,13)(15,16)(17,18)(19,25)(20,22)(21,24)(23,27)(26,31)(28,30)(29,32)(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);(1,3,4,8)(2,5,6,7)(18,22)(19,26)(21,28)(23,31)(25,32)(27,29);(10,13)(14,16)(17,19,20,27)(18,23,22,25)(21,29,28,26)(24,31,30,32);(2,6)(5,7)(9,11,12,15)(10,14,13,16)(18,22)(19,27)(24,30)(26,29)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 19707);