Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#7990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C24×C17 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,25,22,23,20,24)(26,27,29,33,31,35,30,34)(28,36,38,32,39,40,37,41);(19,23)(20,21)(26,28,30,37,31,39,29,38)(27,32,33,40,35,41,34,36);(18,20,22,21)(19,24,23,25)(26,29,31,30)(27,33,35,34)(28,37,39,38)(32,36,41,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 978);