Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C22 |
| direct product | C79×#10462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C79 |
| prime radical | C23×C79 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,4,7)(3,5,8,6)(9,10,14,12)(11,18,21,24)(13,22,16,17)(15,23,19,20)(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);(9,11,14,21)(10,15,12,19)(13,23,16,20)(17,24,22,18);(2,5)(3,8)(6,7)(9,12,13,22,14,10,16,17)(11,19,20,24,21,15,23,18)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 3450);