Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#23532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C22×#41×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C4×C79 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,4)(5,6)(7,17)(8,22)(9,15)(10,14)(11,16)(12,19)(13,26)(18,27)(20,29)(21,28)(23,35)(24,31)(25,30)(32,34)(33,36)(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);(5,7,11,21)(6,12,16,29)(8,23,24,18)(9,20,10,19)(13,27,30,35)(14,28,15,17)(22,32,31,36)(25,33,26,34);(2,4)(5,8,9,25,11,24,10,26)(6,13,14,31,16,30,15,22)(7,18,19,33,21,23,20,34)(12,27,17,32,29,35,28,36);(8,24)(13,30)(18,23)(22,31)(25,26)(27,35)(32,36)(33,34)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 16520);