Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24274 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#1999 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C22⋊C4×C17 ◁ G | |
1034 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)(22,23,25,24)(26,27)(28,33)(29,39)(30,40)(31,35)(32,38)(34,36)(37,41);(18,19)(20,21)(22,24,25,23)(26,28,36,29,31,37,30,38)(27,32,40,41,35,39,34,33);(19,21)(23,24)(28,37)(29,38)(32,39)(33,41);(26,29,36,37,31,38,30,28)(27,33,40,32,35,41,34,39)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18417);