Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13182 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #459 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1947 |
| prime radical | C23×C17 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
280 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)(18,19,24,29,25,30,23,40)(20,31,34,47,35,41,33,45)(21,28,22,38,37,46,36,27)(26,39,42,49,44,48,43,32);(18,20,24,34,25,35,23,33)(19,26,29,42,30,44,40,43)(21,32,22,39,37,49,36,48)(27,41,28,45,38,31,46,47);(18,21,23,36,25,37,24,22)(19,27,29,28,30,38,40,46)(20,32,33,48,35,49,34,39)(26,41,42,45,44,31,43,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6170);