Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#29438 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C17×#376 ◁ G | |
626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(20,24)(21,23)(22,25)(34,35,39,44,40,45,38,43)(36,41,46,42,37,47,48,49);(18,20,21,25)(19,22,23,24)(26,27)(28,31)(29,30)(32,33)(34,36)(35,41)(37,40)(38,48)(39,46)(42,44)(43,49)(45,47);(27,30)(31,33)(34,37,40,36)(35,42,45,49)(38,48,39,46)(41,43,47,44);(19,23)(22,24)(26,28,29,32)(27,31,30,33)(34,38,40,39)(35,43,45,44)(36,46,37,48)(41,42,47,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 22426);