Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C23 |
| direct product | C79×#10198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C79 |
| prime radical | #532×C79 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2,6,10)(3,11,14,15)(4,9,5,8)(7,13,16,12)(17,18,23,28)(19,29,20,31)(21,27,22,26)(24,32,25,30)(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);(1,3,6,14)(2,7,10,16)(4,13,5,12)(8,15,9,11)(17,19,23,20)(18,24,28,25)(21,32,22,30)(26,31,27,29);(3,12)(4,5)(7,11)(8,9)(13,14)(15,16)(17,20)(18,25)(19,23)(21,32)(22,30)(24,28)(26,31)(27,29)2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 3186);