Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#9955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,23)(24,25)(26,27,31,35)(28,36,38,40)(29,32,30,34)(33,39,41,37);(22,25)(27,32)(29,30)(33,36)(34,35)(37,39)(40,41);(18,20)(19,22)(21,24)(23,25)(26,28,31,38)(27,33,35,41)(29,37,30,39)(32,40,34,36)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2943);