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×#10197 |
| 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 | |
524 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,6,3)(4,7,5,8)(9,10,14,18)(11,19,21,24)(12,17,13,16)(15,22,23,20)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,7)(3,8)(4,5)(9,11)(10,15)(12,22)(13,20)(14,21)(16,24)(17,19)(18,23);(1,3,6,2)(4,8,5,7)(9,11,14,21)(10,15,18,23)(12,20,13,22)(16,19,17,24)2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 3185);