Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
986 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)(18,19,23,28)(20,30,34,46)(21,27,22,37)(24,29,40,47)(25,31,43,32)(26,36,38,39)(33,41,35,45)(42,48,44,49);(18,20,23,34)(19,25,28,43)(21,32,22,31)(24,35,40,33)(26,45,38,41)(27,46,37,30)(29,44,47,42)(36,48,39,49);(18,19)(20,25)(21,26)(22,38)(23,28)(24,29)(27,39)(30,48)(31,41)(32,45)(33,42)(34,43)(35,44)(36,37)(40,47)(46,49);(18,21,23,22)(19,26,28,38)(20,31,34,32)(24,36,40,39)(25,41,43,45)(27,29,37,47)(30,44,46,42)(33,48,35,49)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11371);