Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C23×C4 |
| direct product | C79×#33708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| prime radical | C79×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ C2×C4×C8×C79 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2)(3,5)(4,6)(7,8)(9,10)(11,24)(12,17)(13,19)(14,33)(15,35)(16,23)(18,29)(20,25)(21,34)(22,32)(26,40)(27,36)(28,37)(30,39)(31,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(1,3,4,7)(2,5,6,8)(9,11,25,30,13,28,34,31,16,29,15,27,32,26,14,12)(10,17,33,40,22,36,35,18,23,38,21,37,19,39,20,24);(2,6)(5,8)(9,12,14,26,32,27,15,29,16,31,34,28,13,30,25,11)(10,18,20,36,19,40,21,17,23,24,35,39,22,37,33,38);(9,13,16,32)(10,19,23,22)(11,26,29,28)(12,27,31,30)(14,25,34,15)(17,36,38,39)(18,37,24,40)(20,21,35,33)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26696);