Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C79×#1722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C79 |
| prime radical | C2×#127×C79 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×C42×C79 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)(80,81);(83,86)(84,87)(88,89)(90,91,94,97)(92,98,99,105)(93,101,102,96)(95,103,104,100);(90,92,93,100,94,99,102,103)(91,95,96,98,97,104,101,105);(82,83,87,89,85,88,84,86)(92,99)(95,104)(98,105)(100,103)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 12603);