Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#396 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,28,23,29,22,27)(20,30,38,41,33,40,32,25)(21,26,35,42,37,43,36,44)(31,45,46,39,34,48,47,49);(18,20,22,32,23,33,24,38)(19,25,28,30,29,41,27,40)(21,34,36,46,37,31,35,47)(26,39,42,48,43,49,44,45);(18,21)(19,26)(20,31)(22,35)(23,37)(24,36)(25,39)(27,42)(28,44)(29,43)(30,45)(32,46)(33,34)(38,47)(40,48)(41,49);(18,22,23,24)(19,27,29,28)(20,32,33,38)(21,35,37,36)(25,40,41,30)(26,42,43,44)(31,46,34,47)(39,48,49,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16610);