Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18523 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| prime radical | C17×#3475 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,23,26)(20,27,29,32)(21,25,22,30)(24,31,33,28)(34,35,40,44)(36,45,37,48)(38,42,39,43)(41,46,49,47);(18,20,23,29)(19,24,26,33)(21,28,22,31)(25,32,30,27)(34,36,40,37)(35,41,44,49)(38,46,39,47)(42,45,43,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,37,40,36)(35,41,44,49)(38,47,39,46)(42,45,43,48);(34,38,40,39)(35,42,44,43)(36,46,37,47)(41,45,49,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11511);