Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#10377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25)(20,28,30,43)(22,36,34,26)(23,27,35,42)(24,39,40,47)(29,37,41,31)(32,45,33,46)(38,49,48,44);(18,19)(20,29,32,24)(21,25)(22,26)(23,27)(28,31,45,47)(30,41,33,40)(34,36)(35,42)(37,46,39,43)(38,44)(48,49);(18,20,21,33)(19,24,25,41)(22,37,34,47)(23,32,35,30)(26,43,36,45)(27,29,42,40)(28,44,46,49)(31,38,39,48)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3365);