Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#16520 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1590 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)(19,21)(26,27,29,31)(28,32,33,30)(34,35)(36,40)(37,39)(38,41);(22,23,24,25)(34,35,37,39)(36,38,41,40);(22,23)(24,25)(26,28,29,33)(27,30,31,32)(34,35)(36,40)(37,39)(38,41);(18,19)(20,21)(26,27)(28,30)(29,31)(32,33)(34,36)(35,38)(37,41)(39,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 9508);