Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C17×#446 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C17 | C23 |
| commutator | C22 | C22×C42×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle, prime radical | C23×C17 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C17 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(5,6)(7,12)(8,10)(9,11)(13,14,16,15,17,18,20,19);(5,7,9,8)(6,10,11,12);(5,8,9,7)(6,10,11,12)(13,15,16,18,17,19,20,14)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13505);