Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13398 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #481 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C24×C17 | SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,27,31)(24,32,33,50)(25,36,37,53)(26,41,39,30)(28,43,44,34)(29,46,47,40)(35,48,42,51)(38,45,52,49);(18,19)(20,21)(25,37)(29,47)(32,50)(34,43)(36,53)(38,52)(40,46)(48,51);(19,21)(22,24,26,42,27,33,39,35)(23,28,30,49,31,44,41,45)(25,38,40,43,37,52,46,34)(29,48,36,50,47,51,53,32)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6387);