Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C7 |
| abelian | C2×C32×C72×C25 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5 | C2×C32×C5×C72 |
| socle, prime radical | C2×C32×C5×C72 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 22050 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2)(3,4,5)(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);(6,7,8)(41,42,43,44,45,46,47)22050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 151);