Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C26 |
| direct product | C131×#23539 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C131 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| socle | C23×C131 | C22×D4 |
| prime radical | C22×#135×C131 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C131 ◁ C22×C42×C131 ◁ G | |
1494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 155 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 155 points:
(1,2)(3,4)(9,10)(11,12)(13,18)(14,19)(15,20)(16,17)(21,23)(22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155);(5,6)(7,8)(9,11)(10,16)(12,18)(13,21)(14,17)(15,22)(19,24)(20,23);(2,4)(6,8)(9,12,13,23,15,24,14,16)(10,17,19,22,20,21,18,11);(9,13,15,14)(10,18,20,19)(11,21,22,17)(12,23,24,16)8384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 16527);