Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#26853 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | #535×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,21)(12,23)(13,19)(14,18)(15,20)(16,17)(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);(9,11,13,17,15,23,14,22)(10,16,18,21,20,24,19,12);(2,5)(6,8)(9,10,13,18,15,20,14,19)(11,21,17,24,23,12,22,16);(1,3,4,7)(2,6,5,8)(9,12,13,16,15,21,14,24)(10,17,18,23,20,22,19,11)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 19841);