Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
994 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)(18,19,24,21)(20,30,34,44)(22,28,23,36)(25,29,41,37)(26,39,31,32)(27,40,35,38)(33,46,48,42)(43,49,47,45);(18,20,24,34)(19,26,21,31)(22,32,23,39)(25,33,41,48)(27,42,35,46)(28,44,36,30)(29,43,37,47)(38,45,40,49);(18,21,24,19)(20,31,34,26)(22,27,23,35)(25,37,41,29)(28,40,36,38)(30,45,44,49)(32,42,39,46)(33,47,48,43);(18,22,24,23)(19,27,21,35)(20,32,34,39)(25,38,41,40)(26,42,31,46)(28,37,36,29)(30,43,44,47)(33,45,48,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11413);