Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#24798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C2×#135×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
846 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)(8,21)(9,23)(10,27)(11,16)(12,15)(13,19)(14,24)(18,32)(20,29)(22,35)(25,36)(26,30)(28,34)(31,33)(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);(5,7,10,19,11,20,12,8)(6,13,15,17,16,21,27,29)(9,18,24,33,25,34,26,22)(14,28,23,31,30,32,36,35);(2,4)(5,8)(6,13)(7,10)(9,22)(11,19)(12,20)(14,28)(15,17)(16,21)(18,24)(23,31)(25,33)(26,34)(27,29)(30,32)(35,36);(5,9,12,26,11,25,10,24)(6,14,27,36,16,30,15,23)(7,18,8,22,20,34,19,33)(13,28,29,35,21,32,17,31)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17786);