Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#18004 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×M16×C17 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(26,27,29,32,30,33,36,39)(28,31,35,38,34,37,40,41);(18,19,22,24)(20,23,21,25);(18,20,22,21)(19,23,24,25)(26,28,29,35,30,34,36,40)(27,31,32,38,33,37,39,41);(28,34)(31,37)(35,40)(38,41)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10992);