Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
1004 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)(19,24)(20,28)(21,33)(25,38)(26,36)(27,34)(29,44)(31,47)(32,43)(35,46)(37,40)(39,49)(41,45)(42,48);(18,19,22,27)(20,29,32,25)(21,34,33,24)(23,26,30,39)(28,41,43,40)(31,37,48,45)(35,49,46,36)(38,47,44,42);(21,35)(24,36)(31,42)(33,46)(34,49)(37,38)(44,45)(47,48);(18,20,30,43)(19,25,39,41)(21,31,46,47)(22,32,23,28)(24,37,49,44)(26,40,27,29)(33,48,35,42)(34,45,36,38)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11347);