Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C17×#382 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C17 | C23 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C17 ◁ G | |
4286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4);(6,7)(9,10,11,12)(15,19)(17,20);(5,6,8,7)(13,14,16,18)(15,17,19,20);(5,7,8,6)(13,15)(14,17)(16,19)(18,20)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26995);