Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#7053 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C42 |
| commutator | C4 | C4×C16×C17 |
| Frattini, cosocle | C82 | C22×C17 |
| socle, prime radical | C22×C17 | #322 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(18,19,20,24,21,26,28,32,22,25,27,33,29,23,30,31);(19,23,25,26)(20,27)(24,32,33,31)(28,30)(34,35,36,39,37,40,42,45,38,41,43,46,44,47,48,49)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 41);