Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#21484 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | C2×#120 |
| commutator | C23 | C23×C4×C79 |
| Frattini, cosocle | C22×C4 | C24×C79 |
| socle | C2×C79 | C4×#120 |
| prime radical | C79×#3025 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ C22×C8×C79 ◁ G | |
1306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,6,10,7,11,19,5)(3,8,15,22,14,21,29,13)(4,9,18,24,17,23,30,16)(12,25,28,26,27,20,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,3)(2,8)(4,12)(5,13)(6,15)(7,14)(9,20)(10,22)(11,21)(16,26)(17,27)(18,28)(19,29)(23,25)(24,32)(30,31);(1,4)(2,9)(3,12)(5,16)(6,18)(7,17)(8,20)(10,24)(11,23)(13,26)(14,27)(15,28)(19,30)(21,25)(22,32)(29,31);(1,5,6,2,7,10,19,11)(3,13,15,8,14,22,29,21)(4,16,18,9,17,24,30,23)(12,26,28,20,27,32,31,25)4582 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 14472);