Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#18977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C79 |
| prime radical | C79×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2)(3,12)(4,8)(5,9)(6,11)(7,14)(10,15)(13,16)(17,18,24,21)(19,28,20,32)(22,27,23,26)(25,31,29,30)(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);(1,3,6,5)(2,7,11,16)(4,13,15,14)(8,12,10,9)(17,19,24,20)(18,25,21,29)(22,31,23,30)(26,32,27,28);(1,4,6,15)(2,8,11,10)(3,13,5,14)(7,12,16,9)(17,20,24,19)(18,25,21,29)(22,30,23,31)(26,32,27,28);(1,5,6,3)(2,9,11,12)(4,13,15,14)(7,8,16,10)(17,21)(18,24)(19,29)(20,25)(22,27)(23,26)(28,31)(30,32)2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 11965);