Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11285 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #394 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
606 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)(18,19,20,21)(22,23)(24,28,33,40)(25,29,36,43)(26,31)(27,30)(32,39)(34,41,47,52)(35,42)(37,44,49,50)(38,45)(46,51)(48,53);(22,24)(23,28,30,40)(25,35,36,48)(26,34)(27,33)(29,42)(31,41,45,52)(32,37,46,49)(38,47)(39,50)(43,53)(44,51);(22,25)(23,29,30,43)(24,32,33,46)(26,37)(27,36)(28,39)(31,44,45,50)(34,35,47,48)(38,49)(40,51)(41,42)(52,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4273);