Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#25145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C79×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C4×C79 ◁ G | |
996 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)(5,6,9,14,11,16,10,15)(7,12,18,27,20,29,19,28)(8,21,25,13,24,32,23,31)(17,33,35,26,22,36,34,30)(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);(2,4)(5,7,10,19,11,20,9,18)(6,12,15,28,16,29,14,27)(8,22,23,35,24,17,25,34)(13,30,21,36,31,26,32,33);(5,8)(6,13)(7,17)(9,23)(10,25)(11,24)(12,26)(14,21)(15,32)(16,31)(18,34)(19,35)(20,22)(27,33)(28,36)(29,30);(2,4)(5,9,11,10)(6,14,16,15)(7,18,20,19)(8,23,24,25)(12,27,29,28)(13,21,31,32)(17,34,22,35)(26,33,30,36)3397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 18133);