Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3188 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
960 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)(20,30)(21,24)(22,28)(23,37)(25,29)(26,32)(27,39)(31,40)(33,43)(34,46)(35,48)(36,41)(38,42)(44,49)(45,47);(18,20)(19,26)(21,31)(22,32)(23,40)(24,34)(25,35)(27,43)(28,46)(29,45)(30,37)(33,42)(36,48)(38,44)(39,47)(41,49);(18,21,24,19)(20,31,34,26)(22,27,23,36)(25,38,42,29)(28,41,37,39)(30,47,46,49)(32,43,40,48)(33,45,35,44);(18,22,24,23)(19,27,21,36)(20,32,34,40)(25,39,42,41)(26,43,31,48)(28,38,37,29)(30,45,46,44)(33,49,35,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11410);