Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#24799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23,26,29)(24,31,34,37)(25,30,35,28)(27,36,32,33);(22,23,25,28,26,29,35,30)(24,27,33,31,34,32,36,37);(19,21)(22,23)(24,32)(25,28)(26,29)(27,34)(30,35)(31,36)(33,37);(22,24,25,33,26,34,35,36)(23,27,28,31,29,32,30,37)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17787);