Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#13090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C24×C17 ◁ C23×D4×C17 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,30,32,37)(25,28,34,36)(26,29)(27,31)(33,35);(22,24,25,33)(23,27,28,30)(26,32,34,31)(29,35,36,37);(19,21)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6078);