Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#8487 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C17×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21,24,25)(22,23)(26,27,30,34,31,35,29,39)(28,36,37,32,38,33,40,41);(18,20)(19,21)(22,24)(23,25)(26,28)(27,32)(29,40)(30,37)(31,38)(33,34)(35,41)(36,39);(18,21)(19,20)(22,25)(23,24)(26,28)(27,33)(29,37)(30,40)(31,38)(32,34)(35,36)(39,41)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1475);