Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C4×C17×#398 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C17 | C23 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| socle, prime radical | C24×C17 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C17 ◁ G | |
1574 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);(9,10,11,12)(14,17)(18,19);(6,8)(13,14,16,17)(15,19,20,18);(5,6)(7,8)(9,10)(11,12)(13,15,16,20)(14,18,17,19)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6851);