Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11541 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#13083 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#99 |
| commutator | C24 | C22×C4×C79 |
| Frattini, cosocle | C22×D4 | C23×C79 |
| prime radical | C79×#2404 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ C22×#41×C79 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(3,4)(5,6,10,12)(7,13)(8,11,17,18)(9,15)(14,19)(16,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(5,7,13,6,10,15,9,12)(8,14,19,11,17,20,16,18);(2,4)(5,8,10,17)(6,11,12,18)(7,14,15,20)(9,16,13,19)2923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 6071);