Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24430 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#547 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C4×D4×C17 ◁ G | |
1448 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)(18,19,20,21)(26,27)(28,37)(29,33)(30,34)(31,36)(32,38)(35,40)(39,41);(22,23)(24,25)(26,28,31,29)(27,32,36,41)(30,39,40,38)(33,34,37,35);(19,21)(23,25)(26,29,31,28)(27,33,36,37)(30,39,40,38)(32,34,41,35);(27,34)(30,40)(32,37)(33,41)(35,36)(38,39)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17418);