Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23601 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#121 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,26,31,28,32,27,41)(24,33,35,44,37,50,36,29)(25,30,42,47,40,48,39,46)(34,49,52,43,51,45,38,53);(18,19)(20,21)(22,24,27,36,28,37,26,35)(23,29,31,33,32,44,41,50)(25,38,39,51,40,52,42,34)(30,45,47,53,48,49,46,43);(19,21)(22,25)(23,30)(24,34)(26,39)(27,42)(28,40)(29,43)(31,46)(32,48)(33,49)(35,38)(36,52)(37,51)(41,47)(44,53)(45,50);(22,26,28,27)(23,31,32,41)(24,35,37,36)(25,39,40,42)(29,33,44,50)(30,46,48,47)(34,38,51,52)(43,49,53,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16589);