Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C17×#13231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1964 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×#131 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22,30,37)(21,31)(23,38)(24,27)(25,34)(26,32)(28,40,43,49)(29,44,41,36)(33,47,48,42)(35,45)(39,46);(18,20,22,27,24,30,37,19)(21,28,33,39,35,43,48,25)(23,29,36,38,32,41,44,26)(31,34,42,40,45,46,47,49);(18,21,32,46,24,35,23,34)(19,25,38,45,27,39,26,31)(20,28,41,47,30,43,29,42)(22,33,44,49,37,48,36,40)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6219);