Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60140 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C24 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C17×#3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
2722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,31,27,30,37,43)(24,28,34,40,33,39,46,50)(25,29,35,42,36,41,47,51)(32,38,45,49,44,48,52,53);(19,21)(22,24)(23,28)(25,32)(26,34)(27,33)(29,38)(30,39)(31,40)(35,45)(36,44)(37,46)(41,48)(42,49)(43,50)(47,52)(51,53);(22,25,26,35,27,36,37,47)(23,29,31,42,30,41,43,51)(24,32,34,45,33,44,46,52)(28,38,40,49,39,48,50,53);(24,33)(28,39)(32,44)(34,46)(38,48)(40,50)(45,52)(49,53);(23,30)(28,39)(29,41)(31,43)(38,48)(40,50)(42,51)(49,53)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53128);