Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18162 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#18189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C23×C79 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 111 points:
(6,12)(13,16)(17,18,21,25)(19,26,28,31)(20,23,30,24)(22,29,32,27)(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)(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)(15,16)(17,19,21,28)(18,22,25,32)(20,29,30,27)(23,26,24,31);(1,3,5,10)(2,6,8,12)(4,9,11,15)(7,13,14,16);(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,13,12,16)(17,20,21,30)(18,23,25,24)(19,27,28,29)(22,31,32,26)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 11177);