Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#7988 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C2×#95 |
| prime radical | C24×C17 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C42×C17 ◁ G | |
598 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)(18,19,20,23,21,22,24,25)(26,27,29,33,31,35,30,34)(28,36,37,32,39,40,38,41);(19,22)(20,24)(26,28,30,38,31,39,29,37)(27,32,33,40,35,41,34,36);(26,29,31,30)(27,33,35,34)(28,37,39,38)(32,40,41,36)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 976);