Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#25564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| prime radical | C17×#2021 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,24)(21,23)(22,25)(26,27)(28,31)(29,32)(30,33)(34,36)(35,38)(37,39)(40,41);(18,20,21,25)(19,22,23,24)(26,28)(27,31)(29,35)(30,36)(32,38)(33,34)(37,41)(39,40);(26,27)(28,34,36,31)(29,32)(30,33)(35,40,41,38)(37,39);(19,23)(22,24)(26,29,30,37)(27,32,33,39)(28,35,36,41)(31,38,34,40)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18552);