Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C79 · Schur multiplier (H2) = C24×C4 |
| direct product | C79×#21155 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | C22×D4 |
| commutator | C2×C4 | C23×C4×C79 |
| Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C24×C79 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×#117×C79 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,4,3)(5,6)(7,8)(11,17)(12,19)(14,20)(16,22)(18,23)(21,24)(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);(1,3,4,2)(6,8)(9,10)(11,14)(12,16)(13,15)(17,20)(18,21)(19,22)(23,24);(9,11,12,17,13,18,19,23)(10,14,16,20,15,21,22,24);(10,15)(14,21)(16,22)(20,24)5056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 14143);