Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23652 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#397 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,29,22,27)(20,30,32,25,34,41,33,42)(21,35,37,43,38,44,39,26)(31,46,48,49,36,40,47,45);(18,20)(19,25)(21,36)(22,32)(23,33)(24,34)(26,40)(27,41)(28,30)(29,42)(31,38)(35,49)(37,48)(39,47)(43,46)(44,45);(18,21,22,37,24,38,23,39)(19,26,27,35,29,43,28,44)(20,31,33,48,34,36,32,47)(25,40,30,45,42,46,41,49);(18,22,24,23)(19,27,29,28)(20,32,34,33)(21,37,38,39)(25,41,42,30)(26,35,43,44)(31,47,36,48)(40,49,46,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16640);