Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7459 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | D8 |
| commutator | C8 | C2×C16×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle | C2×C17 | #1370 |
| prime radical | C22×C17 | #364 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ C2×C16×C17 ◁ C4×C16×C17 ◁ G | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,21,29,34,43,24,28,39,42,36,45,35,48,25,30,40,44,37,46,33,49,23,41,38,47,32,27,20,31);(18,20,32,38,23,33,37,40,25,35,36,39,24,34,21,22)(19,26,29,43,28,42,45,48,30,44,46,49,41,47,27,31)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 447);