Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C79 · Schur multiplier (H2) = C26 |
| direct product | C2×C79×#1839 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C79 | C23 |
| commutator | C22 | C23×C8×C79 |
| Frattini, cosocle | C22×C4 | C24×C79 |
| socle, prime radical | C24×C79 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C79 ◁ G | |
1134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 20224 |
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);(82,83,84,86,85,87,88,89)(90,91)(92,94)(93,95)(96,97)(98,99)(100,104)(101,102)(103,105);(90,92,93,96)(91,94,95,97)(99,102)(103,104);(91,95)(94,97)(98,100,101,105)(99,103,102,104)8848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 13758);