Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C79 · Schur multiplier (H2) = C23 |
| direct product | C79×#21679 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C79 | C24 |
| commutator | C23 | C23×C4×C79 |
| Frattini, cosocle | C22×C4 | C24×C79 |
| socle, prime radical | C23×C79 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C79 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2)(3,5)(4,6)(7,8)(9,10,12,13)(11,14,15,16)(17,18,23,25,22,26,20,21)(19,27,28,32,30,24,31,29)(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);(1,3,4,7)(2,5,6,8)(10,13)(14,16)(17,19,22,30)(18,24,26,27)(20,31,23,28)(21,32,25,29);(2,6)(5,8)(9,11,12,15)(10,14,13,16)(17,20,22,23)(18,25,26,21)(19,28,30,31)(24,32,27,29);(17,21,20,26,22,25,23,18)(19,29,31,24,30,32,28,27)6004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 14667);