Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10631 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#10633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #397 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #124 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(26,27,30,32,31,35,29,34)(28,36,38,41,37,40,39,33);(18,19,21,24)(20,22,25,23)(27,32)(28,37)(29,30)(33,40)(34,35)(36,41);(19,22)(20,25)(23,24)(26,28,29,38,31,37,30,39)(27,33,34,36,35,41,32,40)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3621);