Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C2×C79×#2064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C24×C79 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C23×C4×C79 ◁ G | |
1006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(7,8,12,15,11,17,10,16)(9,14,20,22,19,21,18,13);(3,4)(5,6)(7,9,10,18,11,19,12,20)(8,13,15,14,17,22,16,21);(4,6)(7,9,11,19)(8,14,17,21)(10,20,12,18)(13,16,22,15)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 16588);