Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#16529 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
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)(19,21)(27,30)(28,32)(34,35,38,37)(36,40,41,39);(22,23,24,25)(34,36)(35,39)(37,40)(38,41);(22,23)(24,25)(26,27)(28,31)(29,30)(32,33)(34,37,38,35)(36,40,41,39);(18,19)(20,21)(26,28,29,32)(27,31,30,33)(34,36)(35,40)(37,39)(38,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 9517);