Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#19909 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C79 |
| prime radical | C79×#3391 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ G | |
638 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)(3,6)(4,7)(5,9)(8,12)(10,13)(11,15)(14,16)(18,22)(19,25)(23,31)(24,26)(27,29)(28,32)(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);(1,3,5,11)(2,6,9,15)(4,10,12,16)(7,13,8,14)(17,18,21,24)(19,26,25,22)(20,28,30,31)(23,27,32,29);(2,7)(4,12)(6,13)(8,9)(10,16)(14,15)(17,19,21,25)(18,22,24,26)(20,27,30,29)(23,31,32,28);(17,20,21,30)(18,23,24,32)(19,27,25,29)(22,31,26,28)3397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 12897);