Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#18960 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C79 |
| prime radical | C79×#3217 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 111 points:
(2,6)(4,11)(7,13)(8,12)(10,15)(14,16)(19,26)(20,29)(22,30)(23,24)(27,28)(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);(1,2,5,8)(3,7,9,14)(4,12,11,6)(10,16,15,13)(17,18)(19,22)(20,23)(21,25)(24,29)(26,32)(27,30)(28,31);(1,3,5,9)(2,7,8,14)(4,10,11,15)(6,13,12,16)(17,19)(18,22)(20,27)(21,28)(23,30)(24,32)(25,31)(26,29);(3,9)(7,14)(10,15)(13,16)(17,20,21,29)(18,23,25,24)(19,27,28,26)(22,30,31,32)2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 11948);