Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#26855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
764 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)(20,25)(21,23)(22,24)(26,27)(28,29)(30,36)(31,35)(32,37)(33,34)(38,40)(39,41);(18,20,22,21)(19,23,24,25)(26,27,31,36,32,37,30,35)(28,29,34,40,39,41,38,33);(18,21,22,20)(19,23,24,25)(26,28,30,38,32,39,31,34)(27,33,35,41,37,40,36,29);(19,24)(23,25)(26,29,30,33,32,41,31,40)(27,34,35,28,37,38,36,39)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 19843);